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Theorem orordi 552
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 536 . . 3 ((𝜑𝜑) ↔ 𝜑)
21orbi1i 542 . 2 (((𝜑𝜑) ∨ (𝜓𝜒)) ↔ (𝜑 ∨ (𝜓𝜒)))
3 or4 550 . 2 (((𝜑𝜑) ∨ (𝜓𝜒)) ↔ ((𝜑𝜓) ∨ (𝜑𝜒)))
42, 3bitr3i 266 1 ((𝜑 ∨ (𝜓𝜒)) ↔ ((𝜑𝜓) ∨ (𝜑𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wo 383
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 197  df-or 385
This theorem is referenced by:  pm4.78  605
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