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Theorem xor3 372
Description: Two ways to express "exclusive or." (Contributed by NM, 1-Jan-2006.)
Assertion
Ref Expression
xor3 (¬ (𝜑𝜓) ↔ (𝜑 ↔ ¬ 𝜓))

Proof of Theorem xor3
StepHypRef Expression
1 pm5.18 371 . . 3 ((𝜑𝜓) ↔ ¬ (𝜑 ↔ ¬ 𝜓))
21con2bii 347 . 2 ((𝜑 ↔ ¬ 𝜓) ↔ ¬ (𝜑𝜓))
32bicomi 214 1 (¬ (𝜑𝜓) ↔ (𝜑 ↔ ¬ 𝜓))
Colors of variables: wff setvar class
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  1467  hadnot  1540  nabbi  2895  symdifass  3851  notzfaus  4838  nmogtmnf  27609  nmopgtmnf  28711  limsucncmpi  32428  aiffnbandciffatnotciffb  40840  axorbciffatcxorb  40841  abnotbtaxb  40851
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