Theorem biimpcd

Description: Deduce a commuted implication from a logical equivalence. (Contributed by NM, 3-May-1994) (Proof shortened by Wolf Lammen, 22-Sep-2013)

	Ref	Expression
Hypothesis	biimpcd.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
Assertion	biimpcd	⊢ ( 𝜓 → ( 𝜑 → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		biimpcd.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2		id	⊢ ( 𝜓 → 𝜓 )
3	2 1	syl5ibcom	⊢ ( 𝜓 → ( 𝜑 → 𝜒 ) )