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Theorem pm2.82 812
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 ax-1 6 . . 3 ((𝜑𝜓) → ((𝜑 ∨ ¬ 𝜒) → (𝜑𝜓)))
2 pm2.24 621 . . . 4 (𝜒 → (¬ 𝜒𝜓))
32orim2d 788 . . 3 (𝜒 → ((𝜑 ∨ ¬ 𝜒) → (𝜑𝜓)))
41, 3jaoi 716 . 2 (((𝜑𝜓) ∨ 𝜒) → ((𝜑 ∨ ¬ 𝜒) → (𝜑𝜓)))
54orim1d 787 1 (((𝜑𝜓) ∨ 𝜒) → (((𝜑 ∨ ¬ 𝜒) ∨ 𝜃) → ((𝜑𝜓) ∨ 𝜃)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 708
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in2 615  ax-io 709
This theorem depends on definitions:  df-bi 117
This theorem is referenced by: (None)
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