Theorem alrimdh 1734

Description: Deduction form of Theorem 19.21 of [Margaris] p. 90, see 19.21 1998 and 19.21h 2000. (Contributed by NM, 10-Feb-1997.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Hypotheses

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

Assertion

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

Proof of Theorem alrimdh

Step	Hyp	Ref	Expression
1		alrimdh.2	. 2 |- ( ps -> A. x ps )
2		alrimdh.1	. . 3 |- ( ph -> A. x ph )
3		alrimdh.3	. . 3 |- ( ph -> ( ps -> ch ) )
4	2, 3	alimdh 1700	. 2 |- ( ph -> ( A. x ps -> A. x ch ) )
5	1, 4	syl5 33	1 |- ( ph -> ( ps -> A. x ch ) )

Syntax hints:   -> wi 4   A.wal 1453

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1680  ax-4 1693

This theorem is referenced by:  alrimdv  1786  ax12indn  32560  gen21nv  37043