Theorem alrimdh 1414

Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (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 1402	. 2 |- ( ph -> ( A. x ps -> A. x ch ) )
5	1, 4	syl5 32	1 |- ( ph -> ( ps -> A. x ch ) )

Syntax hints:   -> wi 4   A.wal 1288

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1382  ax-gen 1384

This theorem is referenced by:  nfimd  1523  alrimdv  1805  moexexdc  2033