Theorem xnor 1306

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

Assertion

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

Proof of Theorem xnor

Step	Hyp	Ref	Expression
1		df-xor 1305	. 2 ⊢ ((φ ⊻ ψ) ↔ ¬ (φ ↔ ψ))
2	1	con2bii 322	1 ⊢ ((φ ↔ ψ) ↔ ¬ (φ ⊻ ψ))

Syntax hints:  ¬ wn 3   ↔ wb 176   ⊻ wxo 1304

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-xor 1305

This theorem is referenced by:  xorneg1  1311  hadbi  1387