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Theorem or4 514
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 509 . . 3 ((ψ (χ θ)) ↔ (χ (ψ θ)))
21orbi2i 505 . 2 ((φ (ψ (χ θ))) ↔ (φ (χ (ψ θ))))
3 orass 510 . 2 (((φ ψ) (χ θ)) ↔ (φ (ψ (χ θ))))
4 orass 510 . 2 (((φ χ) (ψ θ)) ↔ (φ (χ (ψ θ))))
52, 3, 43bitr4i 268 1 (((φ ψ) (χ θ)) ↔ ((φ χ) (ψ θ)))
Colors of variables: wff setvar class
Syntax hints:  wb 176   wo 357
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-or 359
This theorem is referenced by:  or42  515  orordi  516  orordir  517  3or6  1263
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