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Theorem xor2 1494
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 1489 . 2 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
2 nbi2 998 . 2 (¬ (𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))
31, 2bitri 267 1 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 198  wa 387  wo 833  wxo 1488
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 199  df-an 388  df-or 834  df-xor 1489
This theorem is referenced by:  xoror  1495  xornan  1496  cador  1571  saddisjlem  15673  ifpdfxor  39255  dfxor4  39480  nanorxor  40059
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