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

Theorem 3orrot 974
Description: Rotation law for triple disjunction. (Contributed by NM, 4-Apr-1995.)
Assertion
Ref Expression
3orrot ((𝜑𝜓𝜒) ↔ (𝜓𝜒𝜑))

Proof of Theorem 3orrot
StepHypRef Expression
1 orcom 718 . 2 ((𝜑 ∨ (𝜓𝜒)) ↔ ((𝜓𝜒) ∨ 𝜑))
2 3orass 971 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
3 df-3or 969 . 2 ((𝜓𝜒𝜑) ↔ ((𝜓𝜒) ∨ 𝜑))
41, 2, 33bitr4i 211 1 ((𝜑𝜓𝜒) ↔ (𝜓𝜒𝜑))
Colors of variables: wff set class
Syntax hints:  wb 104  wo 698  w3o 967
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-io 699
This theorem depends on definitions:  df-bi 116  df-3or 969
This theorem is referenced by:  3mix2  1157  3mix3  1158  eueq3dc  2900  tprot  3669  sotritrieq  4303  exmidontriimlem3  7179  elnnz  9201  elznn  9207  ztri3or0  9233  zapne  9265
  Copyright terms: Public domain W3C validator