Theorem 3impexpbicomiVD 38115

Description: Virtual deduction proof of 3impexpbicomi 37707. 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 38020	⊢ (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 37706	. . 3 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 ↔ 𝜏)) ↔ (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃)))))
3	2	biimpi 205	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 ↔ 𝜏)) → (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃)))))
4	1, 3	e0a 38020	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃))))

Syntax hints:   → wi 4   ↔ wb 195   ∧ w3a 1031

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 196  df-an 385  df-3an 1033

This theorem is referenced by: (None)