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Theorem pm2.8 823
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 ((φ ψ) → ((¬ ψ χ) → (φ χ)))

Proof of Theorem pm2.8
StepHypRef Expression
1 pm2.53 362 . . 3 ((φ ψ) → (¬ φψ))
21con1d 116 . 2 ((φ ψ) → (¬ ψφ))
32orim1d 812 1 ((φ ψ) → ((¬ ψ χ) → (φ χ)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   wo 357
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 177  df-or 359  df-an 360
This theorem is referenced by: (None)
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