Theorem xor3 346

Description: Two ways to express "exclusive or." (Contributed by NM, 1-Jan-2006.)

Assertion

Ref	Expression
xor3	|- (-. (ph <-> ps) <-> (ph <-> -. ps))

Proof of Theorem xor3

Step	Hyp	Ref	Expression
1		pm5.18 345	. . 3 |- ((ph <-> ps) <-> -. (ph <-> -. ps))
2	1	con2bii 322	. 2 |- ((ph <-> -. ps) <-> -. (ph <-> ps))
3	2	bicomi 193	1 |- (-. (ph <-> ps) <-> (ph <-> -. ps))

This proof depends on syntax axioms:  -. wn 3   <-> wb 176

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177

This theorem is used by:  nbbn  347  pm5.15  859  nbi2  862  mpto2  1534  mtp-xorOLD  1537