Theorem 3impexpbicomi 39622

Description: Inference associated with 3impexpbicom 39621. Derived automatically from 3impexpbicomiVD 40009. (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 215	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜏 ↔ 𝜃))
3	2	3exp 1109	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜏 ↔ 𝜃))))

Syntax hints:   → wi 4   ↔ wb 198   ∧ w3a 1071

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 199  df-an 387  df-3an 1073

This theorem is referenced by:  sbcoreleleq  39677  sbcoreleleqVD  40010