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Theorem xor2 1510
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 1505 . 2 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
2 nbi2 954 . 2 (¬ (𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))
31, 2bitri 264 1 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wo 382  wa 383  wxo 1504
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-or 384  df-an 385  df-xor 1505
This theorem is referenced by:  xoror  1511  xornan  1512  cador  1587  saddisjlem  15233  ifpdfxor  38149  dfxor4  38375  nanorxor  38821
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