Theorem alimdv 1932

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 1579	. 2 |- ( ph -> A. x ph )
2		alimdv.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	alimdh 1520	1 |- ( ph -> ( A. x ps -> A. x ch ) )

Syntax hints:   -> wi 4   A.wal 1400

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1500  ax-gen 1502  ax-17 1579

This theorem is referenced by:  2alimdv  1934  moim  2151  ralimdv2  2620  sstr2  3255  reuss2  3513  ssuni  3955  disjss2  4107  disjss1  4110  disjiun  4123  exmidsssnc  4338  soss  4457  alxfr  4605  ssrel  4861  ssrel2  4863  ssrelrel  4873  iotaval  5347  omnimkv  7489