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Theorem pm5.53 797
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 705 . 2 ((((𝜑𝜓) ∨ 𝜒) → 𝜃) ↔ (((𝜑𝜓) → 𝜃) ∧ (𝜒𝜃)))
2 jaob 705 . . 3 (((𝜑𝜓) → 𝜃) ↔ ((𝜑𝜃) ∧ (𝜓𝜃)))
32anbi1i 455 . 2 ((((𝜑𝜓) → 𝜃) ∧ (𝜒𝜃)) ↔ (((𝜑𝜃) ∧ (𝜓𝜃)) ∧ (𝜒𝜃)))
41, 3bitri 183 1 ((((𝜑𝜓) ∨ 𝜒) → 𝜃) ↔ (((𝜑𝜃) ∧ (𝜓𝜃)) ∧ (𝜒𝜃)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wb 104  wo 703
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 704
This theorem depends on definitions:  df-bi 116
This theorem is referenced by: (None)
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