(P=P) v (P =/= -P) observes the law of excluded middle applied to the laws of logic where the laws of logic are propositions given they are assertions. Either the law of identity is false, in which case P=-P, or the law of non contradiction is false, in which case P=-P.

Either way P=-P and P=/=-P simultaneously. The same can be observed where 1=1 but 1 may equal a horse or a jet. 1=1 and 1=/=1 simultaneously.