First, the laws of logic are not subject to a proof, by virtue of their being self-evident axioms; what that means is, their justification is instrinsic (they justify themselves), not extrinsic (something else justifies them). Second, that is also why they are absolute, or true in all places for all circumstances at all times; as you recognized, any arguments against the laws of logic cannot but use them.
Man is a rational animal who always loses his temper when
called upon to act in accordance with the dictates of reason.
(Oscar Wilde)
called upon to act in accordance with the dictates of reason.
(Oscar Wilde)