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Theorem pm2.82 892
Description: Theorem *2.82 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm2.82 (((𝜑𝜓) ∨ 𝜒) → (((𝜑 ∨ ¬ 𝜒) ∨ 𝜃) → ((𝜑𝜓) ∨ 𝜃)))

Proof of Theorem pm2.82
StepHypRef Expression
1 pm2.24 119 . . . 4 (𝜒 → (¬ 𝜒𝜓))
21orim2d 880 . . 3 (𝜒 → ((𝜑 ∨ ¬ 𝜒) → (𝜑𝜓)))
32jao1i 820 . 2 (((𝜑𝜓) ∨ 𝜒) → ((𝜑 ∨ ¬ 𝜒) → (𝜑𝜓)))
43orim1d 879 1 (((𝜑𝜓) ∨ 𝜒) → (((𝜑 ∨ ¬ 𝜒) ∨ 𝜃) → ((𝜑𝜓) ∨ 𝜃)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 381
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 195  df-or 383  df-an 384
This theorem is referenced by: (None)
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