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Theorem r19.12 2422
 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 2178 . . . 4
2 nfra1 2355 . . . 4
31, 2nfrexxy 2361 . . 3
4 ax-1 5 . . 3
53, 4ralrimi 2390 . 2
6 rsp 2369 . . . . 5
76com12 27 . . . 4
87reximdv 2420 . . 3
98ralimia 2382 . 2
105, 9syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1393  wral 2306  wrex 2307 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312 This theorem is referenced by:  iuniin  3667
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