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 ⊢ φ ∧ ψ ∧ χ → θ ↔ τ
Assertion 3impexpbicomiVD ⊢ φ → ψ → χ → τ ↔ θ

Proof

Step Hyp Ref Expression
1 3impexpbicomiVD.1 ⊢ φ ∧ ψ ∧ χ → θ ↔ τ
2 3impexpbicom ⊢ φ ∧ ψ ∧ χ → θ ↔ τ ↔ φ → ψ → χ → τ ↔ θ
3 2 biimpi ⊢ φ ∧ ψ ∧ χ → θ ↔ τ → φ → ψ → χ → τ ↔ θ
4 1 3 e0a ⊢ φ → ψ → χ → τ ↔ θ