Theorem biimpi

Description: Infer an implication from a logical equivalence. Inference associated with biimp . (Contributed by NM, 29-Dec-1992)

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

Proof

Step	Hyp	Ref	Expression
1		biimpi.1	⊢ ( 𝜑 ↔ 𝜓 )
2		biimp	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜑 → 𝜓 ) )
3	1 2	ax-mp	⊢ ( 𝜑 → 𝜓 )