ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3orcomb Structured version   GIF version

Theorem 3orcomb 893
Description: Commutation law for triple disjunction. (Contributed by Scott Fenton, 20-Apr-2011.)
Assertion
Ref Expression
3orcomb ((φ ψ χ) ↔ (φ χ ψ))

Proof of Theorem 3orcomb
StepHypRef Expression
1 orcom 646 . . 3 ((ψ χ) ↔ (χ ψ))
21orbi2i 678 . 2 ((φ (ψ χ)) ↔ (φ (χ ψ)))
3 3orass 887 . 2 ((φ ψ χ) ↔ (φ (ψ χ)))
4 3orass 887 . 2 ((φ χ ψ) ↔ (φ (χ ψ)))
52, 3, 43bitr4i 201 1 ((φ ψ χ) ↔ (φ χ ψ))
Colors of variables: wff set class
Syntax hints:  wb 98   wo 628   w3o 883
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-io 629
This theorem depends on definitions:  df-bi 110  df-3or 885
This theorem is referenced by:  eueq3dc  2709  sotritrieq  4053
  Copyright terms: Public domain W3C validator