Theorem hbimd 2126

Description: Deduction form of bound-variable hypothesis builder hbim 2127. (Contributed by NM, 14-May-1993.) (Proof shortened by Wolf Lammen, 3-Jan-2018.)

Hypotheses

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

Assertion

Ref	Expression
hbimd	|- ( ph -> ( ( ps -> ch ) -> A. x ( ps -> ch ) ) )

Proof of Theorem hbimd

Step	Hyp	Ref	Expression
1		hbimd.1	. . . 4 |- ( ph -> A. x ph )
2		hbimd.2	. . . 4 |- ( ph -> ( ps -> A. x ps ) )
3	1, 2	nf5dh 2026	. . 3 |- ( ph -> F/ x ps )
4		hbimd.3	. . . 4 |- ( ph -> ( ch -> A. x ch ) )
5	1, 4	nf5dh 2026	. . 3 |- ( ph -> F/ x ch )
6	3, 5	nfimd 1823	. 2 |- ( ph -> F/ x ( ps -> ch ) )
7	6	nf5rd 2066	1 |- ( ph -> ( ( ps -> ch ) -> A. x ( ps -> ch ) ) )

Syntax hints:   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-nf 1710

This theorem is referenced by:  dvelimf-o  34214