Theorem hbimd

Description: Deduction form of bound-variable hypothesis builder hbim . (Contributed by NM, 14-May-1993) (Proof shortened by Wolf Lammen, 3-Jan-2018)

	Ref	Expression
Hypotheses	hbimd.1	|- ( ph -> A. x ph )
	hbimd.2	|- ( ph -> ( ps -> A. x ps ) )
	hbimd.3	|- ( ph -> ( ch -> A. x ch ) )
Assertion	hbimd	|- ( ph -> ( ( ps -> ch ) -> A. x ( ps -> ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		hbimd.1	|- ( ph -> A. x ph )
2		hbimd.2	|- ( ph -> ( ps -> A. x ps ) )
3		hbimd.3	|- ( ph -> ( ch -> A. x ch ) )
4	1 2	nf5dh	|- ( ph -> F/ x ps )
5	1 3	nf5dh	|- ( ph -> F/ x ch )
6	4 5	nfimd	|- ( ph -> F/ x ( ps -> ch ) )
7	6	nf5rd	|- ( ph -> ( ( ps -> ch ) -> A. x ( ps -> ch ) ) )