Theorem hbnd 1545

Description: Deduction form of bound-variable hypothesis builder hbn 1544. (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 1358	. 2 |- ( ph -> A. x ( ps -> A. x ps ) )
4		hbnt 1543	. 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 1241

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-ie2 1383  ax-4 1400  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249

This theorem is referenced by: (None)