Proof A=A

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Circular argument. Materialism is a philosophy based on logic, so what you are saying is, "A logical inference can be considered true if supported by empirical evidence, which can be considered true because of the logical inference of materialism".

There are many who would argue that logical does equal true, because the three laws of logic are all supportive statements, and if one of them is taken as false, everything we know about reality that can be deduced by logic comes crumbling down.

You are right that materialism is based on logic... but we can only assume logic to be correct, as it's very foundation is itself. If logic is 'true'... then everything based off of it is likewise true (in its scenario, EG: If all dogs are mountains, then no dog is not a mountain... not to mean that necessarily it is true that all dogs are mountains (The difference between a 'sound' statement and a 'valid' statement)).

But logic could perhaps be ultimately untrue... we have no way to prove its "truth" except by itself.