Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  3impexpbicomiVD Structured version   Visualization version   GIF version

Theorem 3impexpbicomiVD 43232
Description: Virtual deduction proof of 3impexpbicomi 42854. 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 43146 (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 42853 . . 3 (((𝜑𝜓𝜒) → (𝜃𝜏)) ↔ (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃)))))
32biimpi 215 . 2 (((𝜑𝜓𝜒) → (𝜃𝜏)) → (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃)))))
41, 3e0a 43146 1 (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  w3a 1088
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 206  df-an 398  df-3an 1090
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator