Theorem alrimdv 1899

Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (Contributed by NM, 10-Feb-1997.)

Hypothesis

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

Assertion

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

Distinct variable groups:   ph, x   ps, x

Allowed substitution hint:   ch( x)

Proof of Theorem alrimdv

Step	Hyp	Ref	Expression
1		ax-17 1549	. 2 |- ( ph -> A. x ph )
2		ax-17 1549	. 2 |- ( ps -> A. x ps )
3		alrimdv.1	. 2 |- ( ph -> ( ps -> ch ) )
4	1, 2, 3	alrimdh 1502	1 |- ( ph -> ( ps -> A. x ch ) )

Syntax hints:   -> wi 4   A.wal 1371

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1470  ax-gen 1472  ax-17 1549

This theorem is referenced by:  exmidsssnc  4248  funcnvuni  5344  fliftfun  5867  findcard  6987  findcard2  6988  findcard2s  6989  genprndl  7636  genprndu  7637  seqf1og  10668  bj-inf2vnlem2  15944