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Theorem xor2 1639
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 1634 . 2 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
2 nbi2 1039 . 2 (¬ (𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))
31, 2bitri 266 1 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 197  wa 384  wo 873  wxo 1633
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 198  df-an 385  df-or 874  df-xor 1634
This theorem is referenced by:  xoror  1640  xornan  1641  cador  1717  saddisjlem  15483  ifpdfxor  38534  dfxor4  38759  nanorxor  39204
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