Theorem 3impexpbicomiVD 45624

Description: Virtual deduction proof of 3impexpbicomi 45248. 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 45538	⊢ (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 45247	. . 3 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 ↔ 𝜏)) ↔ (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃)))))
3	2	biimpi 219	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 ↔ 𝜏)) → (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃)))))
4	1, 3	e0a 45538	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃))))

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by: (None)