Theorem xnor

Description: Two ways to write XNOR (exclusive not-or). (Contributed by Mario Carneiro, 4-Sep-2016)

	Ref	Expression
Assertion	xnor	$$⊢\left(\phi \leftrightarrow \psi \right)\leftrightarrow \neg \left(\phi ⊻\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		df-xor	$$⊢\left(\phi ⊻\psi \right)\leftrightarrow \neg \left(\phi \leftrightarrow \psi \right)$$
2	1	con2bii	$$⊢\left(\phi \leftrightarrow \psi \right)\leftrightarrow \neg \left(\phi ⊻\psi \right)$$