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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
StepHypRef Expression
1 nfcv 2619 . . . 4
2 nfra1 2838 . . . 4
31, 2nfrex 2920 . . 3
4 ax-1 6 . . 3
53, 4ralrimi 2857 . 2
6 rsp 2823 . . . . 5
76com12 31 . . . 4
87reximdv 2931 . . 3
98ralimia 2848 . 2
105, 9syl 16 1
 Colors of variables: wff setvar class 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
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