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Theorem pm5.53 726
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 641 . 2 ((((𝜑𝜓) ∨ 𝜒) → 𝜃) ↔ (((𝜑𝜓) → 𝜃) ∧ (𝜒𝜃)))
2 jaob 641 . . 3 (((𝜑𝜓) → 𝜃) ↔ ((𝜑𝜃) ∧ (𝜓𝜃)))
32anbi1i 439 . 2 ((((𝜑𝜓) → 𝜃) ∧ (𝜒𝜃)) ↔ (((𝜑𝜃) ∧ (𝜓𝜃)) ∧ (𝜒𝜃)))
41, 3bitri 177 1 ((((𝜑𝜓) ∨ 𝜒) → 𝜃) ↔ (((𝜑𝜃) ∧ (𝜓𝜃)) ∧ (𝜒𝜃)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  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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