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Theorem an12s 776
Description: Swap two conjuncts in antecedent. The label suffix "s" means that an12 772 is combined with syl 15 (or a variant). (Contributed by NM, 13-Mar-1996.)
Hypothesis
Ref Expression
an12s.1 ((φ (ψ χ)) → θ)
Assertion
Ref Expression
an12s ((ψ (φ χ)) → θ)

Proof of Theorem an12s
StepHypRef Expression
1 an12 772 . 2 ((ψ (φ χ)) ↔ (φ (ψ χ)))
2 an12s.1 . 2 ((φ (ψ χ)) → θ)
31, 2sylbi 187 1 ((ψ (φ χ)) → θ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358
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 177  df-an 360
This theorem is referenced by:  anabsan2  795
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