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When A believes that the proposition p is true, we may say

A subscribes to the proposition that ...

Which verbs may replace the italicized expression without altering the meaning of the sentence?

Answers should be either suitable to academic prose or archaic.

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One may espouse or embrace a proposition, particularly if it is a deeply-held belief.

If the person actively supports the proposition, in addition to simply believing it is true, you could also say that they champion, endorse, or advocate it.

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"Believes"!

There is also "accepts", and possibly in some contexts "adopts".

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A adheres to the proposition that ...

The usage especially fits the general idea supported by subscribing to an idea: one is supporting or attesting to that idea. In the Merriam-Webster dictionary, "Adhere" refers to supporting or assenting to an idea (meaning 2):

1 : to hold fast or stick by or as if by gluing, suction, grasping, or fusing

The stamp failed to adhere to the envelope.

2 : to give support or maintain loyalty

adhere to traditional values

3 : to bind oneself to observance

adhere to the rules

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concurs with, a little more formal than agrees with.

In British English, “agree” is sometimes used with a direct object, e.g., “agree the treaty.”

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