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Theorem xornbi 1318
Description: A consequence of exclusive or. For decidable propositions this is an equivalence, as seen at xornbidc 1323. (Contributed by Jim Kingdon, 10-Mar-2018.)
Assertion
Ref Expression
xornbi ((𝜑𝜓) → ¬ (𝜑𝜓))

Proof of Theorem xornbi
StepHypRef Expression
1 xorbin 1316 . 2 ((𝜑𝜓) → (𝜑 ↔ ¬ 𝜓))
2 pm5.18im 1317 . . 3 ((𝜑𝜓) → ¬ (𝜑 ↔ ¬ 𝜓))
32con2i 590 . 2 ((𝜑 ↔ ¬ 𝜓) → ¬ (𝜑𝜓))
41, 3syl 14 1 ((𝜑𝜓) → ¬ (𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 103  wxo 1307
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115  df-xor 1308
This theorem is referenced by: (None)
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