Theorem xor2 1310

Description: Two ways to express "exclusive or." (Contributed by Mario Carneiro, 4-Sep-2016.)

Assertion

Ref	Expression
xor2	|- ((ph \/_ ps) <-> ((ph \/ ps) /\ -. (ph /\ ps)))

Proof of Theorem xor2

Step	Hyp	Ref	Expression
1		df-xor 1305	. 2 |- ((ph \/_ ps) <-> -. (ph <-> ps))
2		nbi2 862	. 2 |- (-. (ph <-> ps) <-> ((ph \/ ps) /\ -. (ph /\ ps)))
3	1, 2	bitri 240	1 |- ((ph \/_ ps) <-> ((ph \/ ps) /\ -. (ph /\ ps)))

Syntax hints:  -. wn 3   <-> wb 176   \/ wo 357   /\ wa 358   \/_ 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-or 359  df-an 360  df-xor 1305

This theorem is referenced by:  cador  1391  cad1  1398