Laws of Thought

Identity

Note that other philosophers have established the Law of Identity to be a naming of one particular thing. In logic, the law of identity states that each thing is identical with itself. By this it is meant that each thing (be it a universal or a particular) is composed of its own unique set of characteristic qualities or features, which the ancient Greeks called its essence. It is the first of the three classical Laws of Thought.

	∀a: a = a

Excluded Middle

In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is true.

 	⊢. p ∨ ~p

https://ncatlab.org/nlab/show/excluded+middle

Noncontradiction

In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions "p is the case" and "p is not the case" are mutually exclusive.

         ~(p & ~p)