Metamath Proof Explorer


Theorem 3impexpbicomiVD

Description: Virtual deduction proof of 3impexpbicomi . 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:: |- ( ( ph /\ ps /\ ch ) -> ( th <-> ta ) )
qed:1,?: e0a |- ( ph -> ( ps -> ( ch -> ( ta <-> th ) ) ) )
(Contributed by Alan Sare, 31-Dec-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis 3impexpbicomiVD.1 ( ( 𝜑𝜓𝜒 ) → ( 𝜃𝜏 ) )
Assertion 3impexpbicomiVD ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜏𝜃 ) ) ) )

Proof

Step Hyp Ref Expression
1 3impexpbicomiVD.1 ( ( 𝜑𝜓𝜒 ) → ( 𝜃𝜏 ) )
2 3impexpbicom ( ( ( 𝜑𝜓𝜒 ) → ( 𝜃𝜏 ) ) ↔ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜏𝜃 ) ) ) ) )
3 2 biimpi ( ( ( 𝜑𝜓𝜒 ) → ( 𝜃𝜏 ) ) → ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜏𝜃 ) ) ) ) )
4 1 3 e0a ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜏𝜃 ) ) ) )