Theorem xorneg2 1474

Description: The connector \/_ is negated under negation of one argument. (Contributed by Mario Carneiro, 4-Sep-2016.) (Proof shortened by Wolf Lammen, 27-Jun-2020.)

Assertion

Ref	Expression
xorneg2	|- ( ( ph \/_ -. ps ) <-> -. ( ph \/_ ps ) )

Proof of Theorem xorneg2

Step	Hyp	Ref	Expression
1		df-xor 1465	. 2 |- ( ( ph \/_ -. ps ) <-> -. ( ph <-> -. ps ) )
2		pm5.18 371	. 2 |- ( ( ph <-> ps ) <-> -. ( ph <-> -. ps ) )
3		xnor 1466	. 2 |- ( ( ph <-> ps ) <-> -. ( ph \/_ ps ) )
4	1, 2, 3	3bitr2i 288	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:  xorneg1  1475  xorneg  1476