Theorem xorneg 1313

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 1311	. 2 |- ((-. ph \/_ -. ps) <-> -. (ph \/_ -. ps))
2		xorneg2 1312	. . 3 |- ((ph \/_ -. ps) <-> -. (ph \/_ ps))
3	2	con2bii 322	. 2 |- ((ph \/_ ps) <-> -. (ph \/_ -. ps))
4	1, 3	bitr4i 243	1 |- ((-. ph \/_ -. ps) <-> (ph \/_ ps))

Syntax hints:  -. wn 3   <-> wb 176   \/_ wxo 1304

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 177  df-xor 1305

This theorem is referenced by:  hadnot  1393  had0  1403  mtp-xor  1536