Theorem ralimdaa 2859

Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 22-Sep-2003.) (Proof shortened by Wolf Lammen, 29-Dec-2019.)

Hypotheses

Ref	Expression
ralimdaa.1
ralimdaa.2

Assertion

Ref	Expression
ralimdaa

Proof of Theorem ralimdaa

Step	Hyp	Ref	Expression
1		ralimdaa.1	. . 3
2		ralimdaa.2	. . . 4
3	2	ex 434	. . 3
4	1, 3	ralrimi 2857	. 2
5		ralim 2846	. 2
6	4, 5	syl 16	1

Syntax hints:  ->wi 4  /\wa 369  F/wnf 1616  e.wcel 1818  A.wral 2807

This theorem is referenced by:  ralimdvaOLD  2866  eltsk2g  9150  ptcnplem  20122  infrglb  31584  stoweidlem61  31843  stoweid  31845  fourierdlem73  31962

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-ral 2812