Theorem ralrimdv 2573

Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 27-May-1998.)

Hypothesis

Ref	Expression
ralrimdv.1	|- ( ph -> ( ps -> ( x e. A -> ch ) ) )

Assertion

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

Distinct variable groups:   ph, x   ps, x

Allowed substitution hints:   ch( x)   A( x)

Proof of Theorem ralrimdv

Step	Hyp	Ref	Expression
1		nfv 1539	. 2 |- F/ x ph
2		nfv 1539	. 2 |- F/ x ps
3		ralrimdv.1	. 2 |- ( ph -> ( ps -> ( x e. A -> ch ) ) )
4	1, 2, 3	ralrimd 2572	1 |- ( ph -> ( ps -> A. x e. A ch ) )

Syntax hints:   -> wi 4   e. wcel 2164   A.wral 2472

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-4 1521  ax-17 1537

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-ral 2477

This theorem is referenced by:  ralrimdva  2574  ralrimivv  2575  nneneq  6913  fzrevral  10171  islss4  13878  topbas  14235  neipsm  14322  cnpnei  14387  metcnp3  14679