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Theorem pm5.71 902
Description: Theorem *5.71 of [WhiteheadRussell] p. 125. (Contributed by Roy F. Longton, 23-Jun-2005.)
Assertion
Ref Expression
pm5.71 ((ψ → ¬ χ) → (((φ ψ) χ) ↔ (φ χ)))

Proof of Theorem pm5.71
StepHypRef Expression
1 orel2 372 . . . 4 ψ → ((φ ψ) → φ))
2 orc 374 . . . 4 (φ → (φ ψ))
31, 2impbid1 194 . . 3 ψ → ((φ ψ) ↔ φ))
43anbi1d 685 . 2 ψ → (((φ ψ) χ) ↔ (φ χ)))
5 pm2.21 100 . . 3 χ → (χ → ((φ ψ) ↔ φ)))
65pm5.32rd 621 . 2 χ → (((φ ψ) χ) ↔ (φ χ)))
74, 6ja 153 1 ((ψ → ¬ χ) → (((φ ψ) χ) ↔ (φ χ)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 176   wo 357   wa 358
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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