Theorem biimpd

Description: Deduce an implication from a logical equivalence. Deduction associated with biimp and biimpi . (Contributed by NM, 11-Jan-1993)

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

Proof

Step	Hyp	Ref	Expression
1		biimpd.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2		biimp	⊢ ( ( 𝜓 ↔ 𝜒 ) → ( 𝜓 → 𝜒 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )