Theorem xorneg1 1372

Description: \/_ is negated under negation of one argument. (Contributed by Mario Carneiro, 4-Sep-2016.)

Assertion

Ref	Expression
xorneg1	|- ( ( -. ph \/_ ps ) <-> -. ( ph \/_ ps ) )

Proof of Theorem xorneg1

Step	Hyp	Ref	Expression
1		df-xor 1363	. 2 |- ( ( -. ph \/_ ps ) <-> -. ( -. ph <-> ps ) )
2		nbbn 358	. . 3 |- ( ( -. ph <-> ps ) <-> -. ( ph <-> ps ) )
3	2	con2bii 332	. 2 |- ( ( ph <-> ps ) <-> -. ( -. ph <-> ps ) )
4		xnor 1364	. 2 |- ( ( ph <-> ps ) <-> -. ( ph \/_ ps ) )
5	1, 3, 4	3bitr2i 273	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:  xorneg2  1373  xorneg  1374