Theorem 3impexpbicomi 1415

Description: Deduction form of 3impexpbicom 1414. (Contributed by Alan Sare, 31-Dec-2011.)

Hypothesis

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

Assertion

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

Proof of Theorem 3impexpbicomi

Step	Hyp	Ref	Expression
1		3impexpbicomi.1	. . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 ↔ 𝜏))
2	1	bicomd 140	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜏 ↔ 𝜃))
3	2	3exp 1180	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃))))

Syntax hints:   → wi 4   ↔ wb 104   ∧ w3a 962

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 964

This theorem is referenced by: (None)