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Theorem xor2 1310
Description: Two ways to express "exclusive or." (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
xor2 ((φψ) ↔ ((φ ψ) ¬ (φ ψ)))

Proof of Theorem xor2
StepHypRef Expression
1 df-xor 1305 . 2 ((φψ) ↔ ¬ (φψ))
2 nbi2 862 . 2 (¬ (φψ) ↔ ((φ ψ) ¬ (φ ψ)))
31, 2bitri 240 1 ((φψ) ↔ ((φ ψ) ¬ (φ ψ)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176   wo 357   wa 358  wxo 1304
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 177  df-or 359  df-an 360  df-xor 1305
This theorem is referenced by:  cador  1391  cad1  1398
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