Theorem xnor 1306

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

Assertion

Ref	Expression
xnor	|- ((ph <-> ps) <-> -. (ph \/_ ps))

Proof of Theorem xnor

Step	Hyp	Ref	Expression
1		df-xor 1305	. 2 |- ((ph \/_ ps) <-> -. (ph <-> ps))
2	1	con2bii 322	1 |- ((ph <-> ps) <-> -. (ph \/_ ps))

This proof depends on syntax axioms:  -. wn 3   <-> wb 176   \/_ wxo 1304

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is used by:  xorneg1  1311  hadbi  1387