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Theorem pm4.78 565
Description: Theorem *4.78 of [WhiteheadRussell] p. 121. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 19-Nov-2012.)
Assertion
Ref Expression
pm4.78 (((φψ) (φχ)) ↔ (φ → (ψ χ)))

Proof of Theorem pm4.78
StepHypRef Expression
1 orordi 516 . 2 ((¬ φ (ψ χ)) ↔ ((¬ φ ψ) φ χ)))
2 imor 401 . 2 ((φ → (ψ χ)) ↔ (¬ φ (ψ χ)))
3 imor 401 . . 3 ((φψ) ↔ (¬ φ ψ))
4 imor 401 . . 3 ((φχ) ↔ (¬ φ χ))
53, 4orbi12i 507 . 2 (((φψ) (φχ)) ↔ ((¬ φ ψ) φ χ)))
61, 2, 53bitr4ri 269 1 (((φψ) (φχ)) ↔ (φ → (ψ χ)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 176   wo 357
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
This theorem is referenced by: (None)
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