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Theorem orordi 700
Description: Distribution of disjunction over disjunction. (Contributed by NM, 25-Feb-1995.)
Assertion
Ref Expression
orordi ((𝜑 ∨ (𝜓𝜒)) ↔ ((𝜑𝜓) ∨ (𝜑𝜒)))

Proof of Theorem orordi
StepHypRef Expression
1 oridm 684 . . 3 ((𝜑𝜑) ↔ 𝜑)
21orbi1i 690 . 2 (((𝜑𝜑) ∨ (𝜓𝜒)) ↔ (𝜑 ∨ (𝜓𝜒)))
3 or4 698 . 2 (((𝜑𝜑) ∨ (𝜓𝜒)) ↔ ((𝜑𝜓) ∨ (𝜑𝜒)))
42, 3bitr3i 179 1 ((𝜑 ∨ (𝜓𝜒)) ↔ ((𝜑𝜓) ∨ (𝜑𝜒)))
Colors of variables: wff set class
Syntax hints:  wb 102  wo 639
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640
This theorem depends on definitions:  df-bi 114
This theorem is referenced by: (None)
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