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Theorem or12 545
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 pm1.5 544 . 2 ((𝜑 ∨ (𝜓𝜒)) → (𝜓 ∨ (𝜑𝜒)))
2 pm1.5 544 . 2 ((𝜓 ∨ (𝜑𝜒)) → (𝜑 ∨ (𝜓𝜒)))
31, 2impbii 199 1 ((𝜑 ∨ (𝜓𝜒)) ↔ (𝜓 ∨ (𝜑𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wo 383
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-or 385
This theorem is referenced by:  orass  546  or32  549  or4  550  3orcoma  1044  sotrieq  5022  ordzsl  6992  plydivex  23956  socnv  31360  nosepon  31520
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