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Theorem an42 521
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 520 . 2 (((φ ψ) (χ θ)) ↔ ((φ χ) (ψ θ)))
2 ancom 253 . . 3 ((ψ θ) ↔ (θ ψ))
32anbi2i 430 . 2 (((φ χ) (ψ θ)) ↔ ((φ χ) (θ ψ)))
41, 3bitri 173 1 (((φ ψ) (χ θ)) ↔ ((φ χ) (θ ψ)))
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98
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 depends on definitions:  df-bi 110
This theorem is referenced by:  rnlem  882  distrnqg  6371  distrnq0  6441  prcdnql  6466  prcunqu  6467
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