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Theorem pm2.74 909
Description: Theorem *2.74 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Andrew Salmon, 7-May-2011.)
Assertion
Ref Expression
pm2.74 ((𝜓𝜑) → (((𝜑𝜓) ∨ 𝜒) → (𝜑𝜒)))

Proof of Theorem pm2.74
StepHypRef Expression
1 orel2 397 . . 3 𝜓 → ((𝜑𝜓) → 𝜑))
2 ax-1 6 . . 3 (𝜑 → ((𝜑𝜓) → 𝜑))
31, 2ja 173 . 2 ((𝜓𝜑) → ((𝜑𝜓) → 𝜑))
43orim1d 902 1 ((𝜓𝜑) → (((𝜑𝜓) ∨ 𝜒) → (𝜑𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 382
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 197  df-or 384  df-an 385
This theorem is referenced by: (None)
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