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Theorem or42 515
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 514 . 2 (((φ ψ) (χ θ)) ↔ ((φ χ) (ψ θ)))
2 orcom 376 . . 3 ((ψ θ) ↔ (θ ψ))
32orbi2i 505 . 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   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: (None)
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