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Theorem an42 798
Description: Rearrangement of 4 conjuncts. (Contributed by NM, 7-Feb-1996.)
Assertion
Ref Expression
an42 (((φ ψ) (χ θ)) ↔ ((φ χ) (θ ψ)))

Proof of Theorem an42
StepHypRef Expression
1 an4 797 . 2 (((φ ψ) (χ θ)) ↔ ((φ χ) (ψ θ)))
2 ancom 437 . . 3 ((ψ θ) ↔ (θ ψ))
32anbi2i 675 . 2 (((φ χ) (ψ θ)) ↔ ((φ χ) (θ ψ)))
41, 3bitri 240 1 (((φ ψ) (χ θ)) ↔ ((φ χ) (θ ψ)))
Colors of variables: wff setvar class
Syntax hints:  wb 176   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:  rnlem  931  fnpprod  5843
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