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Theorem pm4.14 561
Description: Theorem *4.14 of [WhiteheadRussell] p. 117. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 23-Oct-2012.)
Assertion
Ref Expression
pm4.14 (((φ ψ) → χ) ↔ ((φ ¬ χ) → ¬ ψ))

Proof of Theorem pm4.14
StepHypRef Expression
1 con34b 283 . . 3 ((ψχ) ↔ (¬ χ → ¬ ψ))
21imbi2i 303 . 2 ((φ → (ψχ)) ↔ (φ → (¬ χ → ¬ ψ)))
3 impexp 433 . 2 (((φ ψ) → χ) ↔ (φ → (ψχ)))
4 impexp 433 . 2 (((φ ¬ χ) → ¬ ψ) ↔ (φ → (¬ χ → ¬ ψ)))
52, 3, 43bitr4i 268 1 (((φ ψ) → χ) ↔ ((φ ¬ χ) → ¬ ψ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 176   wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
This theorem is referenced by:  pm3.37  562
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