Theorem hbxfrbi

Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. See hbxfreq for equality version. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

	Ref	Expression
Hypotheses	hbxfrbi.1	|- ( ph <-> ps )
	hbxfrbi.2	|- ( ps -> A. x ps )
Assertion	hbxfrbi	|- ( ph -> A. x ph )

Proof

Step	Hyp	Ref	Expression
1		hbxfrbi.1	|- ( ph <-> ps )
2		hbxfrbi.2	|- ( ps -> A. x ps )
3	1	albii	|- ( A. x ph <-> A. x ps )
4	2 1 3	3imtr4i	|- ( ph -> A. x ph )