Theorem alimdh 1396

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 1387	. 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 1282

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1376  ax-gen 1378

This theorem is referenced by:  alrimdh  1408  hbald  1420  alimd  1454  hbimd  1505  dral1  1658  sbiedh  1710  ax16  1734  ax16i  1779  alimdv  1800