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Theorem r19.12 2811
 Description: Theorem 19.12 of [Margaris] p. 89 with restricted quantifiers. (Contributed by NM, 15-Oct-2003.) (Proof shortened by Andrew Salmon, 30-May-2011.)
Assertion
Ref Expression
r19.12
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()

Proof of Theorem r19.12
StepHypRef Expression
1 nfcv 2571 . . . 4
2 nfra1 2748 . . . 4
31, 2nfrex 2753 . . 3
4 ax-1 5 . . 3
53, 4ralrimi 2779 . 2
6 rsp 2758 . . . . 5
76com12 29 . . . 4
87reximdv 2809 . . 3
98ralimia 2771 . 2
105, 9syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1725  wral 2697  wrex 2698 This theorem is referenced by:  iuniin  4095  ucncn  18303  ftc1a  19909  rngoid  21959  rngmgmbs4  21993 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703
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