Theorem impbii

Description: Infer an equivalence from an implication and its converse. Inference associated with impbi . (Contributed by NM, 29-Dec-1992)

	Ref	Expression
Hypotheses	impbii.1	|- ( ph -> ps )
	impbii.2	|- ( ps -> ph )
Assertion	impbii	|- ( ph <-> ps )

Proof

Step	Hyp	Ref	Expression
1		impbii.1	|- ( ph -> ps )
2		impbii.2	|- ( ps -> ph )
3		impbi	|- ( ( ph -> ps ) -> ( ( ps -> ph ) -> ( ph <-> ps ) ) )
4	1 2 3	mp2	|- ( ph <-> ps )