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Theorem 3impexp 1311
 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 1306 . 2 (((𝜑𝜓𝜒) → 𝜃) → (𝜑 → (𝜓 → (𝜒𝜃))))
3 id 22 . . 3 ((𝜑 → (𝜓 → (𝜒𝜃))) → (𝜑 → (𝜓 → (𝜒𝜃))))
433impd 1303 . 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 1054 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 1056 This theorem is referenced by:  cotr2g  13761  bnj978  31145  3impexpbicom  39002  3impexpbicomVD  39406
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