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Theorem pm2.8 890
Description: Theorem *2.8 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Jan-2013.)
Assertion
Ref Expression
pm2.8 ((𝜑𝜓) → ((¬ 𝜓𝜒) → (𝜑𝜒)))

Proof of Theorem pm2.8
StepHypRef Expression
1 pm2.53 386 . . 3 ((𝜑𝜓) → (¬ 𝜑𝜓))
21con1d 137 . 2 ((𝜑𝜓) → (¬ 𝜓𝜑))
32orim1d 879 1 ((𝜑𝜓) → ((¬ 𝜓𝜒) → (𝜑𝜒)))
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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