Theorem xor3 372

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		pm5.18 371	. . 3 |- ( ( ph <-> ps ) <-> -. ( ph <-> -. ps ) )
2	1	con2bii 347	. 2 |- ( ( ph <-> -. ps ) <-> -. ( ph <-> ps ) )
3	2	bicomi 214	1 |- ( -. ( ph <-> ps ) <-> ( ph <-> -. ps ) )

Syntax hints:   -. wn 3   <-> wb 196

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 197

This theorem is referenced by:  nbbn  373  pm5.15  933  nbi2  936  xorass  1468  hadnot  1541  nabbi  2896  symdifass  3853  notzfaus  4840  nmogtmnf  27625  nmopgtmnf  28727  limsucncmpi  32444  aiffnbandciffatnotciffb  41071  axorbciffatcxorb  41072  abnotbtaxb  41082