ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  or12 GIF version

Theorem or12 716
Description: Swap two disjuncts. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 14-Nov-2012.)
Assertion
Ref Expression
or12 ((𝜑 ∨ (𝜓𝜒)) ↔ (𝜓 ∨ (𝜑𝜒)))

Proof of Theorem or12
StepHypRef Expression
1 pm1.5 715 . 2 ((𝜑 ∨ (𝜓𝜒)) → (𝜓 ∨ (𝜑𝜒)))
2 pm1.5 715 . 2 ((𝜓 ∨ (𝜑𝜒)) → (𝜑 ∨ (𝜓𝜒)))
31, 2impbii 124 1 ((𝜑 ∨ (𝜓𝜒)) ↔ (𝜓 ∨ (𝜑𝜒)))
Colors of variables: wff set class
Syntax hints:  wb 103  wo 662
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-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  orass  717  or32  720  or4  721
  Copyright terms: Public domain W3C validator