Theorem xor3 363

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		pm5.18 362	. . 3 |- ( ( ph <-> ps ) <-> -. ( ph <-> -. ps ) )
2	1	con2bii 338	. 2 |- ( ( ph <-> -. ps ) <-> -. ( ph <-> ps ) )
3	2	bicomi 207	1 |- ( -. ( ph <-> ps ) <-> ( ph <-> -. ps ) )

Syntax hints:   -. wn 3   <-> wb 189

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 190

This theorem is referenced by:  nbbn  364  pm5.15  905  nbi2  908  xorass  1419  hadnot  1516  nabbi  2737  symdifass  3684  notzfaus  4595  nmogtmnf  26467  nmopgtmnf  27577  limsucncmpi  31155  aiffnbandciffatnotciffb  38626  axorbciffatcxorb  38627  abnotbtaxb  38638