Theorem hbnd 1633

Description: Deduction form of bound-variable hypothesis builder hbn 1632. (Contributed by NM, 3-Jan-2002.)

Hypotheses

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

Assertion

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

Proof of Theorem hbnd

Step	Hyp	Ref	Expression
1		hbnd.1	. . 3 |- ( ph -> A. x ph )
2		hbnd.2	. . 3 |- ( ph -> ( ps -> A. x ps ) )
3	1, 2	alrimih 1445	. 2 |- ( ph -> A. x ( ps -> A. x ps ) )
4		hbnt 1631	. 2 |- ( A. x ( ps -> A. x ps ) -> ( -. ps -> A. x -. ps ) )
5	3, 4	syl 14	1 |- ( ph -> ( -. ps -> A. x -. ps ) )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1329

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-5 1423  ax-gen 1425  ax-ie2 1470  ax-4 1487  ax-ial 1514

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337

This theorem is referenced by: (None)