Theorem 3impexpbicomiVD 44878

Description: Virtual deduction proof of 3impexpbicomi 44501. 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::	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 ↔ 𝜏))
qed:1,?: e0a 44792	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃))))

(Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
3impexpbicomiVD.1	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 ↔ 𝜏))

Assertion

Ref	Expression
3impexpbicomiVD	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃))))

Proof of Theorem 3impexpbicomiVD

Step	Hyp	Ref	Expression
1		3impexpbicomiVD.1	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 ↔ 𝜏))
2		3impexpbicom 44500	. . 3 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 ↔ 𝜏)) ↔ (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃)))))
3	2	biimpi 216	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 ↔ 𝜏)) → (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃)))))
4	1, 3	e0a 44792	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃))))

Syntax hints:   → wi 4   ↔ wb 206   ∧ w3a 1087

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 207  df-an 396  df-3an 1089

This theorem is referenced by: (None)