Theorem xorneg 1374

Description: \/_ is unchanged under negation of both arguments. (Contributed by Mario Carneiro, 4-Sep-2016.)

Assertion

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

Proof of Theorem xorneg

Step	Hyp	Ref	Expression
1		xorneg1 1372	. 2 |- ( ( -. ph \/_ -. ps ) <-> -. ( ph \/_ -. ps ) )
2		xorneg2 1373	. . 3 |- ( ( ph \/_ -. ps ) <-> -. ( ph \/_ ps ) )
3	2	con2bii 332	. 2 |- ( ( ph \/_ ps ) <-> -. ( ph \/_ -. ps ) )
4	1, 3	bitr4i 252	1 |- ( ( -. ph \/_ -. ps ) <-> ( ph \/_ ps ) )

Syntax hints:   -. wn 3   <-> wb 184   \/_ wxo 1362

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 185  df-xor 1363

This theorem is referenced by:  hadnot  1446  had0  1456