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Theorem xor2 1618
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 1613 . 2 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
2 nbi2 1001 . 2 (¬ (𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))
31, 2bitri 264 1 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wa 382  wo 836  wxo 1612
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  df-an 383  df-or 837  df-xor 1613
This theorem is referenced by:  xoror  1619  xornan  1620  cador  1695  saddisjlem  15394  ifpdfxor  38358  dfxor4  38584  nanorxor  39030
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