Theorem alimdh 1745

Description: Deduction form of Theorem 19.20 of [Margaris] p. 90, see alim 1738. (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 1743	. 2 |- ( A. x ph -> ( A. x ps -> A. x ch ) )
4	1, 3	syl 17	1 |- ( ph -> ( A. x ps -> A. x ch ) )

Syntax hints:   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1722  ax-4 1737

This theorem is referenced by:  alrimdh  1790  alimdv  1845  hbald  2041  alimd  2081  alimdOLD  2191  dral1-o  34189  ax12indalem  34230  ax12inda2ALT  34231