Theorem ibi

Description: Inference that converts a biconditional implied by one of its arguments, into an implication. (Contributed by NM, 17-Oct-2003)

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

Proof

Step	Hyp	Ref	Expression
1		ibi.1	⊢ ( 𝜑 → ( 𝜑 ↔ 𝜓 ) )
2		id	⊢ ( 𝜑 → 𝜑 )
3	2 1	mpbid	⊢ ( 𝜑 → 𝜓 )