Theorem excxor 1309

Description: This tautology shows that xor is really exclusive. (Contributed by FL, 22-Nov-2010.)

Assertion

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

Proof of Theorem excxor

Step	Hyp	Ref	Expression
1		df-xor 1305	. 2 |- ((ph \/_ ps) <-> -. (ph <-> ps))
2		xor 861	. 2 |- (-. (ph <-> ps) <-> ((ph /\ -. ps) \/ (ps /\ -. ph)))
3		ancom 437	. . 3 |- ((ps /\ -. ph) <-> (-. ph /\ ps))
4	3	orbi2i 505	. 2 |- (((ph /\ -. ps) \/ (ps /\ -. ph)) <-> ((ph /\ -. ps) \/ (-. ph /\ ps)))
5	1, 2, 4	3bitri 262	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: (None)