Theorem al2imi 1446

Description: Inference quantifying antecedent, nested antecedent, and consequent. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
al2imi.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
al2imi	|- ( A. x ph -> ( A. x ps -> A. x ch ) )

Proof of Theorem al2imi

Step	Hyp	Ref	Expression
1		al2imi.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	alimi 1443	. 2 |- ( A. x ph -> A. x ( ps -> ch ) )
3		alim 1445	. 2 |- ( A. x ( ps -> ch ) -> ( A. x ps -> A. x ch ) )
4	2, 3	syl 14	1 |- ( A. x ph -> ( A. x ps -> A. x ch ) )

Syntax hints:   -> wi 4   A.wal 1341

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1435  ax-gen 1437

This theorem is referenced by:  alanimi  1447  alimdh  1455  albi  1456  19.30dc  1615  19.33b2  1617  hbnt  1641  ax10o  1703  spimth  1723  sbi1v  1879  ralim  2525  ceqsalt  2752  intss  3845