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Theorem xor3 383
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 pm5.18 382 . . 3 ((𝜑𝜓) ↔ ¬ (𝜑 ↔ ¬ 𝜓))
21con2bii 357 . 2 ((𝜑 ↔ ¬ 𝜓) ↔ ¬ (𝜑𝜓))
32bicomi 223 1 (¬ (𝜑𝜓) ↔ (𝜑 ↔ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 205
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 206
This theorem is referenced by:  nbbn  384  pm5.15  1010  nbi2  1013  xorass  1513  hadnot  1602  nabbi  3044  nmogtmnf  29420  nmopgtmnf  30518  limsucncmpi  34730  wl-3xorbi  35757  wl-3xornot  35765  aiffnbandciffatnotciffb  44758  axorbciffatcxorb  44759  abnotbtaxb  44769  afv2orxorb  45079  line2ylem  46456  line2xlem  46458
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