ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  xornbi GIF version

Theorem xornbi 1274
Description: A consequence of exclusive or. For decidable propositions this is an equivalence, as seen at xornbidc 1279. (Contributed by Jim Kingdon, 10-Mar-2018.)
Assertion
Ref Expression
xornbi ((φψ) → ¬ (φψ))

Proof of Theorem xornbi
StepHypRef Expression
1 xorbin 1272 . 2 ((φψ) → (φ ↔ ¬ ψ))
2 pm5.18im 1273 . . 3 ((φψ) → ¬ (φ ↔ ¬ ψ))
32con2i 557 . 2 ((φ ↔ ¬ ψ) → ¬ (φψ))
41, 3syl 14 1 ((φψ) → ¬ (φψ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 98  wxo 1265
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110  df-xor 1266
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator