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Theorem pm4.87 567
 Description: Theorem *4.87 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Eric Schmidt, 26-Oct-2006.)
Assertion
Ref Expression
pm4.87 (((((φ ψ) → χ) ↔ (φ → (ψχ))) ((φ → (ψχ)) ↔ (ψ → (φχ)))) ((ψ → (φχ)) ↔ ((ψ φ) → χ)))

Proof of Theorem pm4.87
StepHypRef Expression
1 impexp 433 . . 3 (((φ ψ) → χ) ↔ (φ → (ψχ)))
2 bi2.04 350 . . 3 ((φ → (ψχ)) ↔ (ψ → (φχ)))
31, 2pm3.2i 441 . 2 ((((φ ψ) → χ) ↔ (φ → (ψχ))) ((φ → (ψχ)) ↔ (ψ → (φχ))))
4 impexp 433 . . 3 (((ψ φ) → χ) ↔ (ψ → (φχ)))
54bicomi 193 . 2 ((ψ → (φχ)) ↔ ((ψ φ) → χ))
63, 5pm3.2i 441 1 (((((φ ψ) → χ) ↔ (φ → (ψχ))) ((φ → (ψχ)) ↔ (ψ → (φχ)))) ((ψ → (φχ)) ↔ ((ψ φ) → χ)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ 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-an 360 This theorem is referenced by: (None)
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