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Theorem ralunb 3124
 Description: Restricted quantification over a union. (Contributed by Scott Fenton, 12-Apr-2011.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
ralunb

Proof of Theorem ralunb
StepHypRef Expression
1 elun 3084 . . . . . 6
21imbi1i 227 . . . . 5
3 jaob 631 . . . . 5
42, 3bitri 173 . . . 4
54albii 1359 . . 3
6 19.26 1370 . . 3
75, 6bitri 173 . 2
8 df-ral 2311 . 2
9 df-ral 2311 . . 3
10 df-ral 2311 . . 3
119, 10anbi12i 433 . 2
127, 8, 113bitr4i 201 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wo 629  wal 1241   wcel 1393  wral 2306   cun 2915 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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-v 2559  df-un 2922 This theorem is referenced by:  ralun  3125  ralprg  3421  raltpg  3423  ralunsn  3568
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