Theorem hbnd

Description: Deduction form of bound-variable hypothesis builder hbn . (Contributed by NM, 3-Jan-2002)

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

Proof

Step	Hyp	Ref	Expression
1		hbnd.1	|- ( ph -> A. x ph )
2		hbnd.2	|- ( ph -> ( ps -> A. x ps ) )
3	1 2	alrimih	|- ( ph -> A. x ( ps -> A. x ps ) )
4		hbnt	|- ( A. x ( ps -> A. x ps ) -> ( -. ps -> A. x -. ps ) )
5	3 4	syl	|- ( ph -> ( -. ps -> A. x -. ps ) )