Theorem xor3 358

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		pm5.18 357	. . 3 |- ( ( ph <-> ps ) <-> -. ( ph <-> -. ps ) )
2	1	con2bii 333	. 2 |- ( ( ph <-> -. ps ) <-> -. ( ph <-> ps ) )
3	2	bicomi 205	1 |- ( -. ( ph <-> ps ) <-> ( ph <-> -. ps ) )

Syntax hints:   -. wn 3   <-> wb 187

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 188

This theorem is referenced by:  nbbn  359  pm5.15  897  nbi2  900  xorass  1404  hadnot  1500  nabbi  2756  nabbiOLD  2757  symdifass  3699  notzfaus  4591  nmogtmnf  26282  nmopgtmnf  27382  limsucncmpi  30916  aiffnbandciffatnotciffb  37924  axorbciffatcxorb  37925  abnotbtaxb  37936