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

Theorem 3orcomb 905
Description: Commutation law for triple disjunction. (Contributed by Scott Fenton, 20-Apr-2011.)
Assertion
Ref Expression
3orcomb ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))

Proof of Theorem 3orcomb
StepHypRef Expression
1 orcom 657 . . 3 ((𝜓𝜒) ↔ (𝜒𝜓))
21orbi2i 689 . 2 ((𝜑 ∨ (𝜓𝜒)) ↔ (𝜑 ∨ (𝜒𝜓)))
3 3orass 899 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
4 3orass 899 . 2 ((𝜑𝜒𝜓) ↔ (𝜑 ∨ (𝜒𝜓)))
52, 3, 43bitr4i 205 1 ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))
Colors of variables: wff set class
Syntax hints:  wb 102  wo 639  w3o 895
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640
This theorem depends on definitions:  df-bi 114  df-3or 897
This theorem is referenced by:  eueq3dc  2737  sotritrieq  4089
  Copyright terms: Public domain W3C validator