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Theorem pm2.82 712
Description: Theorem *2.82 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm2.82 (((φ ψ) χ) → (((φ ¬ χ) θ) → ((φ ψ) θ)))

Proof of Theorem pm2.82
StepHypRef Expression
1 ax-1 5 . . 3 ((φ ψ) → ((φ ¬ χ) → (φ ψ)))
2 pm2.24 539 . . . 4 (χ → (¬ χψ))
32orim2d 689 . . 3 (χ → ((φ ¬ χ) → (φ ψ)))
41, 3jaoi 623 . 2 (((φ ψ) χ) → ((φ ¬ χ) → (φ ψ)))
54orim1d 688 1 (((φ ψ) χ) → (((φ ¬ χ) θ) → ((φ ψ) θ)))
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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