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Theorem 3impexpbicomiVD 39407
Description: Virtual deduction proof of 3impexpbicomi 39003. 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 39316 (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 39002 . . 3 (((𝜑𝜓𝜒) → (𝜃𝜏)) ↔ (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃)))))
32biimpi 206 . 2 (((𝜑𝜓𝜒) → (𝜃𝜏)) → (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃)))))
41, 3e0a 39316 1 (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃))))
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: (None)
  Copyright terms: Public domain W3C validator