Theorem alimdv 1800

Description: Deduction from Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 3-Apr-1994.)

Hypothesis

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

Assertion

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

Distinct variable group:   ph, x

Allowed substitution hints:   ps( x)   ch( x)

Proof of Theorem alimdv

Step	Hyp	Ref	Expression
1		ax-17 1459	. 2 |- ( ph -> A. x ph )
2		alimdv.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	alimdh 1396	1 |- ( 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  ax-17 1459

This theorem is referenced by:  2alimdv  1802  moim  2005  ralimdv2  2431  sstr2  3006  reuss2  3244  ssuni  3623  disjss2  3769  disjss1  3772  soss  4069  alxfr  4211  ssrel  4446  ssrel2  4448  ssrelrel  4458  iotaval  4898