Theorem r19.12 2983

Description: Restricted quantifier version of 19.12 1950. (Contributed by NM, 15-Oct-2003.) (Proof shortened by Andrew Salmon, 30-May-2011.)

Assertion

Ref	Expression
r19.12

Distinct variable groups:   ,   ,   ,

Proof of Theorem r19.12

Step	Hyp	Ref	Expression
1		nfcv 2619	. . . 4
2		nfra1 2838	. . . 4
3	1, 2	nfrex 2920	. . 3
4		ax-1 6	. . 3
5	3, 4	ralrimi 2857	. 2
6		rsp 2823	. . . . 5
7	6	com12 31	. . . 4
8	7	reximdv 2931	. . 3
9	8	ralimia 2848	. 2
10	5, 9	syl 16	1

Syntax hints:  ->wi 4  e.wcel 1818  A.wral 2807  E.wrex 2808

This theorem is referenced by:  iuniin  4341  ucncn  20788  ftc1a  22438  rngoid  25385  rngmgmbs4  25419  heicant  30049  intimass  37768  intimag  37770

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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813