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Theorem ancom1s 780
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
an32s.1 (((φ ψ) χ) → θ)
Assertion
Ref Expression
ancom1s (((ψ φ) χ) → θ)

Proof of Theorem ancom1s
StepHypRef Expression
1 pm3.22 436 . 2 ((ψ φ) → (φ ψ))
2 an32s.1 . 2 (((φ ψ) χ) → θ)
31, 2sylan 457 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: (None)
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