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Theorem 3impexp 1452
Description: Version of impexp 461 for a triple conjunction. (Contributed by Alan Sare, 31-Dec-2011.)
Assertion
Ref Expression
3impexp (((𝜑𝜓𝜒) → 𝜃) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))

Proof of Theorem 3impexp
StepHypRef Expression
1 id 22 . . 3 (((𝜑𝜓𝜒) → 𝜃) → ((𝜑𝜓𝜒) → 𝜃))
213expd 1447 . 2 (((𝜑𝜓𝜒) → 𝜃) → (𝜑 → (𝜓 → (𝜒𝜃))))
3 id 22 . . 3 ((𝜑 → (𝜓 → (𝜒𝜃))) → (𝜑 → (𝜓 → (𝜒𝜃))))
433impd 1442 . 2 ((𝜑 → (𝜓 → (𝜒𝜃))) → ((𝜑𝜓𝜒) → 𝜃))
52, 4impbii 199 1 (((𝜑𝜓𝜒) → 𝜃) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  w3a 1072
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 197  df-an 385  df-3an 1074
This theorem is referenced by:  cotr2g  13916  bnj978  31326  3impexpbicom  39187  3impexpbicomVD  39591
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