Theorem ibir

Description: Inference that converts a biconditional implied by one of its arguments, into an implication. (Contributed by NM, 22-Jul-2004)

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

Proof

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