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

Theorem xoror 1340
Description: XOR implies OR. (Contributed by BJ, 19-Apr-2019.)
Assertion
Ref Expression
xoror ((𝜑𝜓) → (𝜑𝜓))

Proof of Theorem xoror
StepHypRef Expression
1 xoranor 1338 . 2 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ (¬ 𝜑 ∨ ¬ 𝜓)))
21simplbi 270 1 ((𝜑𝜓) → (𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 680  wxo 1336
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681
This theorem depends on definitions:  df-bi 116  df-xor 1337
This theorem is referenced by:  mtpxor  1387
  Copyright terms: Public domain W3C validator