Theorem alrimdv 1804

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 1464	. 2 |- ( ph -> A. x ph )
2		ax-17 1464	. 2 |- ( ps -> A. x ps )
3		alrimdv.1	. 2 |- ( ph -> ( ps -> ch ) )
4	1, 2, 3	alrimdh 1413	1 |- ( ph -> ( ps -> A. x ch ) )

Syntax hints:   -> wi 4   A.wal 1287

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1381  ax-gen 1383  ax-17 1464

This theorem is referenced by:  funcnvuni  5083  fliftfun  5575  findcard  6602  findcard2  6603  findcard2s  6604  genprndl  7078  genprndu  7079  bj-inf2vnlem2  11821