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	|- ( ph -> ( ph <-> ps ) )
Assertion	ibi	|- ( ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		ibi.1	|- ( ph -> ( ph <-> ps ) )
2		id	|- ( ph -> ph )
3	2 1	mpbid	|- ( ph -> ps )