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Theorem pm5.53 833
Description: Theorem *5.53 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.53 ((((𝜑𝜓) ∨ 𝜒) → 𝜃) ↔ (((𝜑𝜃) ∧ (𝜓𝜃)) ∧ (𝜒𝜃)))

Proof of Theorem pm5.53
StepHypRef Expression
1 jaob 818 . 2 ((((𝜑𝜓) ∨ 𝜒) → 𝜃) ↔ (((𝜑𝜓) → 𝜃) ∧ (𝜒𝜃)))
2 jaob 818 . . 3 (((𝜑𝜓) → 𝜃) ↔ ((𝜑𝜃) ∧ (𝜓𝜃)))
32anbi1i 727 . 2 ((((𝜑𝜓) → 𝜃) ∧ (𝜒𝜃)) ↔ (((𝜑𝜃) ∧ (𝜓𝜃)) ∧ (𝜒𝜃)))
41, 3bitri 263 1 ((((𝜑𝜓) ∨ 𝜒) → 𝜃) ↔ (((𝜑𝜃) ∧ (𝜓𝜃)) ∧ (𝜒𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 195  wo 382  wa 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 196  df-or 384  df-an 385
This theorem is referenced by: (None)
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