Theorem al2imi 1468

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 1465	. 2 |- ( A. x ph -> A. x ( ps -> ch ) )
3		alim 1467	. 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 1361

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1457  ax-gen 1459

This theorem is referenced by:  alanimi  1469  alimdh  1477  albi  1478  19.30dc  1637  19.33b2  1639  hbnt  1663  ax10o  1725  spimth  1745  sbi1v  1901  ralim  2546  ceqsalt  2775  intss  3877