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Theorem 3impexp 1366
Description: impexp 433 with a 3-conjunct antecedent. (Contributed by Alan Sare, 31-Dec-2011.)
Assertion
Ref Expression
3impexp (((φ ψ χ) → θ) ↔ (φ → (ψ → (χθ))))

Proof of Theorem 3impexp
StepHypRef Expression
1 id 19 . . 3 (((φ ψ χ) → θ) → ((φ ψ χ) → θ))
213expd 1168 . 2 (((φ ψ χ) → θ) → (φ → (ψ → (χθ))))
3 id 19 . . 3 ((φ → (ψ → (χθ))) → (φ → (ψ → (χθ))))
433impd 1165 . 2 ((φ → (ψ → (χθ))) → ((φ ψ χ) → θ))
52, 4impbii 180 1 (((φ ψ χ) → θ) ↔ (φ → (ψ → (χθ))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   w3a 934
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  df-3an 936
This theorem is referenced by:  3impexpbicom  1367
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