Theorem al2imi 1458

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 1455	. 2 |- ( A. x ph -> A. x ( ps -> ch ) )
3		alim 1457	. 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 1351

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1447  ax-gen 1449

This theorem is referenced by:  alanimi  1459  alimdh  1467  albi  1468  19.30dc  1627  19.33b2  1629  hbnt  1653  ax10o  1715  spimth  1735  sbi1v  1891  ralim  2536  ceqsalt  2765  intss  3867