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Theorem orordir 690
Description: Distribution of disjunction over disjunction. (Contributed by NM, 25-Feb-1995.)
Assertion
Ref Expression
orordir (((φ ψ) χ) ↔ ((φ χ) (ψ χ)))

Proof of Theorem orordir
StepHypRef Expression
1 oridm 673 . . 3 ((χ χ) ↔ χ)
21orbi2i 678 . 2 (((φ ψ) (χ χ)) ↔ ((φ ψ) χ))
3 or4 687 . 2 (((φ ψ) (χ χ)) ↔ ((φ χ) (ψ χ)))
42, 3bitr3i 175 1 (((φ ψ) χ) ↔ ((φ χ) (ψ χ)))
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:  elznn0  8036
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