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Theorem or12 682
Description: Swap two disjuncts. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 14-Nov-2012.)
Assertion
Ref Expression
or12 ((φ (ψ χ)) ↔ (ψ (φ χ)))

Proof of Theorem or12
StepHypRef Expression
1 pm1.5 681 . 2 ((φ (ψ χ)) → (ψ (φ χ)))
2 pm1.5 681 . 2 ((ψ (φ χ)) → (φ (ψ χ)))
31, 2impbii 117 1 ((φ (ψ χ)) ↔ (ψ (φ χ)))
Colors of variables: wff set class
Syntax hints:  wb 98   wo 628
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
This theorem is referenced by:  orass  683  or32  686  or4  687
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