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Theorem xor3 371
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 pm5.18 370 . . 3 ((𝜑𝜓) ↔ ¬ (𝜑 ↔ ¬ 𝜓))
21con2bii 346 . 2 ((𝜑 ↔ ¬ 𝜓) ↔ ¬ (𝜑𝜓))
32bicomi 213 1 (¬ (𝜑𝜓) ↔ (𝜑 ↔ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 195
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 196
This theorem is referenced by:  nbbn  372  pm5.15  929  nbi2  932  xorass  1460  hadnot  1532  nabbi  2884  symdifass  3815  notzfaus  4761  nmogtmnf  26803  nmopgtmnf  27905  limsucncmpi  31408  aiffnbandciffatnotciffb  39514  axorbciffatcxorb  39515  abnotbtaxb  39525
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