Worswick, C.J.

The City of Olympia suspended one of its police officers for 1 day without pay, purportedly for cause. The Olympia Police Guild asserted a grievance under its collective bargaining agreement with the City, challenging whether the City had cause for the discipline. When the City failed to respond, the Guild invoked arbitration proceedings under the grievance procedure and, when the City still did not respond, sued for specific performance to compel arbitration. It. now appeals summary judgment dismissing its action.

The Guild contended in superior court, as it does here, that whether the City had cause for the suspension specifically was an arbitrable issue under the collective bargaining agreement. The City contended that the agreement is ambiguous, and it presented extrinsic evidence purporting to show that the parties meant to exclude disciplinary actions from arbitration. The trial court agreed with the City. We do not. We reverse, holding that the agreement is not ambiguous, ‘and that well-settled law requires that the *558 agreement be construed as requiring arbitration of the cause issue.

Article VII of the collective bargaining agreement provides

B. For the purpose of this Agreement, a grievance is defined as only those disputes involving the interpretation, application, or alleged violation of any provision of this Agreement, . . ..

(Italics ours.) Article IV, titled "Management rights", provides that the City has " [t]he right to discipline, discharge, or suspend employees for cause; . . .".

Article IV of the agreement only gives the City a limited disciplinary prerogative; it requires cause for discipline. It follows that, if the City had no cause for the suspension in dispute, its action was a violation of the collective bargaining agreement. The subject of cause, therefore, was an arbitrable issue. The agreement is unambiguous and extrinsic evidence is not required to interpret it. See St. Yves v. Mid State Bank, 111 Wn.2d 374, 378, 757 P.2d 1384 (1988).

The City seems to concede that the agreement excerpts set forth above are unambiguous, but it argues that an ambiguity appears upon reading the entirety of Article IV. 1 The City asserts that subjecting any issue classified as a management prerogative under Article IV to the grievance and arbitration procedure opens to arbitration anything the City does under the authority of that provision. This could *559 not have been intended, it says, because management prerogatives were considered sacrosanct by the contracting parties.

The language of Article IV simply does not support the City's argument. There is no suggestion in that language that, other than cause for discipline, any management prerogative is subject to arbitration. Allowing arbitration for one issue in no way attenuates other management prerogatives.

Although the trial court's ruling was based upon the court's conclusion that the agreement was ambiguous, a new principle, interjected by a recent decision, must be considered. Extrinsic evidence may be admitted to aid in the interpretation of an unambiguous agreement under the recently adopted "context rule.” Berg v. Hudesman, 115 Wn.2d 657, 801 P.2d 222 (1990). "Interpretation," as opposed to "construction," means ascertaining the intent of the parties. Berg, 115 Wn.2d at 663. We believe, though, that the intent of the parties to be divined by application of the context rule has to do with their real meeting of the minds, as opposed to the insufficient written expression of their intent. Unilateral and subjective beliefs about the impact of a written contract do not represent the intent of the parties. Dwelley v. Chesterfield, 88 Wn.2d 331, 335, 560 P.2d 353 (1977) ("unexpressed impressions are meaningless when attempting to ascertain the mutual intentions''); see also Multicare Med. Ctr. v. Department of Social & Health Servs., 114 Wn.2d 572, 586-87, 790 P.2d 124 (1990) (unexpressed subjective intentions are irrelevant in discerning mutual assent). The summary judgment record in this case contains no extrinsic evidence showing any meeting of the parties' minds that is inconsistent with the plain words of their agreement. 2 The agreement must, therefore, be con strued — i.e., its legal effect determined {Berg, 115 Wn.2d at 663) — in light of well-settled labor law.

*560 The arbitrability of labor disputes in Washington is controlled by federal law. Local Union 77, Int'l Bhd. of Elec. Workers v. PUD 1, 40 Wn. App. 61, 63, 696 P.2d 1264 (1985). There is a strong presumption that all disputes arising under a collective bargaining agreement are subject to arbitration; that presumption holds unless negated expressly or by clear implication. United Steelworkers v. Warrior & Gulf Nav. Co., 363 U.S. 574, 581, 4 L. Ed. 2d 1409, 80 S. Ct. 1347 (1960). The City has shown nothing in this case tending to overcome this strong presumption.

We have considered, and we find without merit, the City's additional arguments in support of its position. 3

Reversed.

Petrich and Alexander, JJ., concur.

Article IV reads:

"The Guild recognizes the prerogative of the City to manage or administer the Police Department in accordance with its responsibilities, powers, and authority, subject to other provisions of this Agreement. City prerogatives include, but are not limited to, the following items:

"1. The right to establish rules and regulations;

"2. The right to determine methods of operating and the introduction of new equipment;

"3. The right to discipline, discharge or suspend employees for cause;

"4. The right to determine schedules of work and to establish the methods and processes by which work is to be performed; and

"5. The right to schedule overtime work.”

The record includes: (1) the parties' collective bargaining agreements from 1975 until the present; (2) grievances filed pursuant to the collective bargaining *560 agreements; (3) documents from various appeals of Guild members who sought resolution of their disputes before the civil service commission; (4) a memorandum setting out changes proposed by the Guild upon renewal of the 1979 contract, along with the City's response to those proposals; (5) a letter written by the City Manager setting out the City's interpretation of the contract; and (6) an affidavit of the Guild's president indicating his understanding that management rights disputes would be subject to the grievance procedures. At best, this evidence shows the parties' unilateral views, but falls short of proving mutual "intent of the parties."

One such argument, superficially appealing but flawed in substance, deserves brief mention. The City contends that by allowing the cause issue to be presented to an arbitrator, we will be allowing the arbitrator to determine arbitrability of that issue, something only a court can do, thus putting the City in a "Catch 22" situation. We are not, of course, doing anything of the sort. The arbitrator will only deal with whether cause existed. We decide, as only a court can, that the issue is subject to arbitration.