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Theorem xor2 1513
Description: Two ways to express "exclusive or". (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
xor2 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))

Proof of Theorem xor2
StepHypRef Expression
1 df-xor 1507 . 2 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
2 nbi2 1013 . 2 (¬ (𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))
31, 2bitri 274 1 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 205  wa 396  wo 844  wxo 1506
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  df-an 397  df-or 845  df-xor 1507
This theorem is referenced by:  xoror  1514  xornan  1515  cador  1614  saddisjlem  16161  wl-df4-3mintru2  35646  ifpdfxor  41065  dfxor4  41336  nanorxor  41885
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