Theorem xor3 674

Description: Two ways to express "exclusive or."

Assertion

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

Proof of Theorem xor3

Step	Hyp	Ref	Expression
1		pm5.18 660	. . 3 |- ((ph <-> ps) <-> -. (ph <-> -. ps))
2	1	con2bii 221	. 2 |- ((ph <-> -. ps) <-> -. (ph <-> ps))
3	2	bicomi 172	1 |- (-. (ph <-> ps) <-> (ph <-> -. ps))

Syntax hints:  -. wn 2   <-> wb 146

This theorem is referenced by:  notzfaus 2741  nmogtmnf 8433  nmopgtmnf 9795

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225

Copyright terms: Public domain