Theorem xnor 1466

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 1465	. 2 |- ( ( ph \/_ ps ) <-> -. ( ph <-> ps ) )
2	1	con2bii 347	1 |- ( ( ph <-> ps ) <-> -. ( ph \/_ ps ) )

Syntax hints:   -. wn 3   <-> wb 196   \/_ wxo 1464

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 197  df-xor 1465

This theorem is referenced by:  xorass  1468  xorneg2  1474  hadbi  1537  had0  1543  elsymdifxor  3850  tsxo1  33944  tsxo2  33945