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Theorem 3impexp 1342
Description: impexp 254 with a 3-conjunct antecedent. (Contributed by Alan Sare, 31-Dec-2011.)
Assertion
Ref Expression
3impexp (((𝜑𝜓𝜒) → 𝜃) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))

Proof of Theorem 3impexp
StepHypRef Expression
1 id 19 . . 3 (((𝜑𝜓𝜒) → 𝜃) → ((𝜑𝜓𝜒) → 𝜃))
213expd 1132 . 2 (((𝜑𝜓𝜒) → 𝜃) → (𝜑 → (𝜓 → (𝜒𝜃))))
3 id 19 . . 3 ((𝜑 → (𝜓 → (𝜒𝜃))) → (𝜑 → (𝜓 → (𝜒𝜃))))
433impd 1129 . 2 ((𝜑 → (𝜓 → (𝜒𝜃))) → ((𝜑𝜓𝜒) → 𝜃))
52, 4impbii 121 1 (((𝜑𝜓𝜒) → 𝜃) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 102  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  3impexpbicom  1343
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