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Theorem rexun 3520
 Description: Restricted existential quantification over union. (Contributed by Jeff Madsen, 5-Jan-2011.)
Assertion
Ref Expression
rexun

Proof of Theorem rexun
StepHypRef Expression
1 df-rex 2704 . 2
2 19.43 1615 . . 3
3 elun 3481 . . . . . 6
43anbi1i 677 . . . . 5
5 andir 839 . . . . 5
64, 5bitri 241 . . . 4
76exbii 1592 . . 3
8 df-rex 2704 . . . 4
9 df-rex 2704 . . . 4
108, 9orbi12i 508 . . 3
112, 7, 103bitr4i 269 . 2
121, 11bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177   wo 358   wa 359  wex 1550   wcel 1725  wrex 2699   cun 3311 This theorem is referenced by:  rexprg  3851  rextpg  3853  iunxun  4165  oarec  6798  zornn0g  8378  rpnnen2  12818  vdwlem6  13347  cmpfi  17464 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 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rex 2704  df-v 2951  df-un 3318
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