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Theorem orordir 746
Description: Distribution of disjunction over disjunction. (Contributed by NM, 25-Feb-1995.)
Assertion
Ref Expression
orordir (((𝜑𝜓) ∨ 𝜒) ↔ ((𝜑𝜒) ∨ (𝜓𝜒)))

Proof of Theorem orordir
StepHypRef Expression
1 oridm 729 . . 3 ((𝜒𝜒) ↔ 𝜒)
21orbi2i 734 . 2 (((𝜑𝜓) ∨ (𝜒𝜒)) ↔ ((𝜑𝜓) ∨ 𝜒))
3 or4 743 . 2 (((𝜑𝜓) ∨ (𝜒𝜒)) ↔ ((𝜑𝜒) ∨ (𝜓𝜒)))
42, 3bitr3i 185 1 (((𝜑𝜓) ∨ 𝜒) ↔ ((𝜑𝜒) ∨ (𝜓𝜒)))
Colors of variables: wff set class
Syntax hints:  wb 104  wo 680
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  elznn0  9023
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