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Theorem r19.12 2618
 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 2385 . . . 4
2 nfra1 2555 . . . 4
31, 2nfrex 2560 . . 3
4 ax-1 7 . . 3
53, 4ralrimi 2586 . 2
6 ra4 2565 . . . . 5
76com12 29 . . . 4
87reximdv 2616 . . 3
98ralimia 2578 . 2
105, 9syl 17 1
 Colors of variables: wff set class Syntax hints:   wi 6   wcel 1621  wral 2509  wrex 2510 This theorem is referenced by:  iuniin  3813  ftc1a  19216  rngoid  20880  rngmgmbs4  20914 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ral 2513  df-rex 2514
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