Theorem xor3 357

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		pm5.18 356	. . 3 |- ( ( ph <-> ps ) <-> -. ( ph <-> -. ps ) )
2	1	con2bii 332	. 2 |- ( ( ph <-> -. ps ) <-> -. ( ph <-> ps ) )
3	2	bicomi 202	1 |- ( -. ( ph <-> ps ) <-> ( ph <-> -. ps ) )

Syntax hints:   -. wn 3   <-> wb 184

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 185

This theorem is referenced by:  nbbn  358  pm5.15  884  nbi2  887  nabbi  2781  nabbiOLD  2782  notzfaus  4568  nmogtmnf  24315  nmopgtmnf  25417  symdifass  27995  limsucncmpi  28428  aiffnbandciffatnotciffb  30059  axorbciffatcxorb  30060  abnotbtaxb  30071