Theorem alimdh 1443

Description: Deduction from Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 4-Jan-2002.)

Hypotheses

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

Assertion

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

Proof of Theorem alimdh

Step	Hyp	Ref	Expression
1		alimdh.1	. 2 |- ( ph -> A. x ph )
2		alimdh.2	. . 3 |- ( ph -> ( ps -> ch ) )
3	2	al2imi 1434	. 2 |- ( A. x ph -> ( A. x ps -> A. x ch ) )
4	1, 3	syl 14	1 |- ( ph -> ( A. x ps -> A. x ch ) )

Syntax hints:   -> wi 4   A.wal 1329

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1423  ax-gen 1425

This theorem is referenced by:  alrimdh  1455  hbald  1467  alimd  1501  hbimd  1552  dral1  1708  sbiedh  1760  ax16  1785  ax16i  1830  alimdv  1851