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Theorem pm4.79 566
Description: Theorem *4.79 of [WhiteheadRussell] p. 121. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 27-Jun-2013.)
Assertion
Ref Expression
pm4.79 (((ψφ) (χφ)) ↔ ((ψ χ) → φ))

Proof of Theorem pm4.79
StepHypRef Expression
1 id 19 . . 3 ((ψφ) → (ψφ))
2 id 19 . . 3 ((χφ) → (χφ))
31, 2jaoa 496 . 2 (((ψφ) (χφ)) → ((ψ χ) → φ))
4 simplim 143 . . . 4 (¬ (ψφ) → ψ)
5 pm3.3 431 . . . 4 (((ψ χ) → φ) → (ψ → (χφ)))
64, 5syl5 28 . . 3 (((ψ χ) → φ) → (¬ (ψφ) → (χφ)))
76orrd 367 . 2 (((ψ χ) → φ) → ((ψφ) (χφ)))
83, 7impbii 180 1 (((ψφ) (χφ)) ↔ ((ψ χ) → φ))
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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