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Theorem or4 675
Description: Rearrangement of 4 disjuncts. (Contributed by NM, 12-Aug-1994.)
Assertion
Ref Expression
or4 (((φ ψ) (χ θ)) ↔ ((φ χ) (ψ θ)))

Proof of Theorem or4
StepHypRef Expression
1 or12 670 . . 3 ((ψ (χ θ)) ↔ (χ (ψ θ)))
21orbi2i 666 . 2 ((φ (ψ (χ θ))) ↔ (φ (χ (ψ θ))))
3 orass 671 . 2 (((φ ψ) (χ θ)) ↔ (φ (ψ (χ θ))))
4 orass 671 . 2 (((φ χ) (ψ θ)) ↔ (φ (χ (ψ θ))))
52, 3, 43bitr4i 201 1 (((φ ψ) (χ θ)) ↔ ((φ χ) (ψ θ)))
Colors of variables: wff set class
Syntax hints:  wb 98   wo 616
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 617
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  or42  676  orordi  677  orordir  678  3or6  1201  swoer  6041  apcotr  7198
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