Theorem al2imi 1387

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 1384	. 2 |- ( A. x ph -> A. x ( ps -> ch ) )
3		alim 1386	. 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 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:  alanimi  1388  alimdh  1396  albi  1397  19.30dc  1558  19.33b2  1560  hbnt  1583  ax10o  1643  spimth  1663  sbi1v  1812  ralim  2422  ceqsalt  2625  intss  3657