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Theorem pm2.8 710
Description: Theorem *2.8 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
pm2.8 ((φ ψ) → ((¬ ψ χ) → (φ χ)))

Proof of Theorem pm2.8
StepHypRef Expression
1 pm1.4 633 . . 3 ((φ ψ) → (ψ φ))
21ord 630 . 2 ((φ ψ) → (¬ ψφ))
32orim1d 688 1 ((φ ψ) → ((¬ ψ χ) → (φ χ)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wo 616
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 533  ax-io 617
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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