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Theorem ancom2s 485
Description: Inference commuting a nested conjunction in antecedent. (Contributed by NM, 24-May-2006.) (Proof shortened by Wolf Lammen, 24-Nov-2012.)
Hypothesis
Ref Expression
an12s.1 ((φ (ψ χ)) → θ)
Assertion
Ref Expression
ancom2s ((φ (χ ψ)) → θ)

Proof of Theorem ancom2s
StepHypRef Expression
1 pm3.22 252 . 2 ((χ ψ) → (ψ χ))
2 an12s.1 . 2 ((φ (ψ χ)) → θ)
31, 2sylan2 270 1 ((φ (χ ψ)) → θ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem is referenced by:  an42s  508  ordsuc  4214  xpexr2m  4678  f1elima  5326  f1imaeq  5328  isosolem  5377  caovlem2d  5605  2ndconst  5755  prarloclem4  6339  mulsub  6998  leltadd  7041  divmul24ap  7278
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