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Theorem 3impexpbicomiVD 41498
Description: Virtual deduction proof of 3impexpbicomi 41120. 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:: ((𝜑𝜓𝜒) → (𝜃 𝜏))
qed:1,?: e0a 41412 (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃))))
(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 41119 . . 3 (((𝜑𝜓𝜒) → (𝜃𝜏)) ↔ (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃)))))
32biimpi 219 . 2 (((𝜑𝜓𝜒) → (𝜃𝜏)) → (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃)))))
41, 3e0a 41412 1 (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  w3a 1084
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 210  df-an 400  df-3an 1086
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator