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Theorem 3impexpbicomiVD 40009
Description: Virtual deduction proof of 3impexpbicomi 39622. The following user's proof is completed by invoking mmj2's unify command and using mmj2's StepSelector to pick all remaining steps of the Metamath proof.
 h1:: ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 ↔ 𝜏)) qed:1,?: e0a 39923 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃))))
(Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
3impexpbicomiVD.1 ((𝜑𝜓𝜒) → (𝜃𝜏))
Assertion
Ref Expression
3impexpbicomiVD (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃))))

Proof of Theorem 3impexpbicomiVD
StepHypRef Expression
1 3impexpbicomiVD.1 . 2 ((𝜑𝜓𝜒) → (𝜃𝜏))
2 3impexpbicom 39621 . . 3 (((𝜑𝜓𝜒) → (𝜃𝜏)) ↔ (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃)))))
32biimpi 208 . 2 (((𝜑𝜓𝜒) → (𝜃𝜏)) → (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃)))))
41, 3e0a 39923 1 (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃))))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 198   ∧ w3a 1071 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 199  df-an 387  df-3an 1073 This theorem is referenced by: (None)
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