Theorem xorneg2 1312

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

Assertion

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

Proof of Theorem xorneg2

Step	Hyp	Ref	Expression
1		xorneg1 1311	. 2 |- ((-. ps \/_ ph) <-> -. (ps \/_ ph))
2		xorcom 1307	. 2 |- ((ph \/_ -. ps) <-> (-. ps \/_ ph))
3		xorcom 1307	. . 3 |- ((ph \/_ ps) <-> (ps \/_ ph))
4	3	notbii 287	. 2 |- (-. (ph \/_ ps) <-> -. (ps \/_ ph))
5	1, 2, 4	3bitr4i 268	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:  xorneg  1313  hadnot  1393