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Theorem an4s 799
Description: Inference rearranging 4 conjuncts in antecedent. (Contributed by NM, 10-Aug-1995.)
Hypothesis
Ref Expression
an4s.1 (((φ ψ) (χ θ)) → τ)
Assertion
Ref Expression
an4s (((φ χ) (ψ θ)) → τ)

Proof of Theorem an4s
StepHypRef Expression
1 an4 797 . 2 (((φ χ) (ψ θ)) ↔ ((φ ψ) (χ θ)))
2 an4s.1 . 2 (((φ ψ) (χ θ)) → τ)
31, 2sylbi 187 1 (((φ χ) (ψ θ)) → τ)
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:  an42s  800  anandis  803  anandirs  804  2mo  2282  fnun  5190  f1co  5265  f1oun  5305  f1oco  5309  fntxp  5805  fnpprod  5844  f1opprod  5845  enprmaplem3  6079  sbthlem3  6206  fnfrec  6321
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