Theorem xnor

Description: Two ways to write XNOR. (Contributed by Mario Carneiro, 4-Sep-2016)

	Ref	Expression
Assertion	xnor	⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ ¬ ( 𝜑 ⊻ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		df-xor	⊢ ( ( 𝜑 ⊻ 𝜓 ) ↔ ¬ ( 𝜑 ↔ 𝜓 ) )
2	1	con2bii	⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ ¬ ( 𝜑 ⊻ 𝜓 ) )