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Theorem or42 688
Description: Rearrangement of 4 disjuncts. (Contributed by NM, 10-Jan-2005.)
Assertion
Ref Expression
or42 (((φ ψ) (χ θ)) ↔ ((φ χ) (θ ψ)))

Proof of Theorem or42
StepHypRef Expression
1 or4 687 . 2 (((φ ψ) (χ θ)) ↔ ((φ χ) (ψ θ)))
2 orcom 646 . . 3 ((ψ θ) ↔ (θ ψ))
32orbi2i 678 . 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:  wb 98   wo 628
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  reapcotr  7382
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