Theorem al2imi 1482

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 1479	. 2 |- ( A. x ph -> A. x ( ps -> ch ) )
3		alim 1481	. 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 1371

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1471  ax-gen 1473

This theorem is referenced by:  alanimi  1483  alimdh  1491  albi  1492  19.30dc  1651  19.33b2  1653  hbnt  1677  ax10o  1739  spimth  1759  sbi1v  1916  ralim  2566  ceqsalt  2800  intss  3912