Theorem alimdv 1759

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 1419	. 2 |- ( ph -> A. x ph )
2		alimdv.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	alimdh 1356	1 |- ( ph -> ( A. x ps -> A. x ch ) )

Syntax hints:   -> wi 4   A.wal 1241

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1336  ax-gen 1338  ax-17 1419

This theorem is referenced by:  2alimdv  1761  moim  1964  ralimdv2  2389  sstr2  2952  reuss2  3217  ssuni  3602  disjss2  3748  disjss1  3751  soss  4051  alxfr  4193  ssrel  4428  ssrel2  4430  ssrelrel  4440  iotaval  4878