Theorem 3impexpbicomi

Description: Inference associated with 3impexpbicom . Derived automatically from 3impexpbicomiVD . (Contributed by Alan Sare, 31-Dec-2011)

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

Proof

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