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Theorem 3orrot 902
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 657 . 2 ((𝜑 ∨ (𝜓𝜒)) ↔ ((𝜓𝜒) ∨ 𝜑))
2 3orass 899 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
3 df-3or 897 . 2 ((𝜓𝜒𝜑) ↔ ((𝜓𝜒) ∨ 𝜑))
41, 2, 33bitr4i 205 1 ((𝜑𝜓𝜒) ↔ (𝜓𝜒𝜑))
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:  3mix2  1085  3mix3  1086  eueq3dc  2738  tprot  3491  sotritrieq  4090  elnnz  8312  elznn  8318  ztri3or0  8344  zapne  8373
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