Theorem alrimdv 1929

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 1579	. 2 |- ( ph -> A. x ph )
2		ax-17 1579	. 2 |- ( ps -> A. x ps )
3		alrimdv.1	. 2 |- ( ph -> ( ps -> ch ) )
4	1, 2, 3	alrimdh 1532	1 |- ( ph -> ( ps -> A. x ch ) )

This proof depends on syntax axioms:   -> wi 4   A.wal 1400

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1500  ax-gen 1502  ax-17 1579

This theorem is used by:  exmidsssnc  4340  funcnvuni  5450  fliftfun  6002  findcard  7192  findcard2  7193  findcard2s  7194  genprndl  7888  genprndu  7889  seqf1og  10958  bj-inf2vnlem2  16997