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Theorem rexun 3683
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 2813 . 2
2 19.43 1693 . . 3
3 elun 3644 . . . . . 6
43anbi1i 695 . . . . 5
5 andir 868 . . . . 5
64, 5bitri 249 . . . 4
76exbii 1667 . . 3
8 df-rex 2813 . . . 4
9 df-rex 2813 . . . 4
108, 9orbi12i 521 . . 3
112, 7, 103bitr4i 277 . 2
121, 11bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  \/wo 368  /\wa 369  E.wex 1612  e.wcel 1818  E.wrex 2808  u.cun 3473
This theorem is referenced by:  rexprg  4079  rextpg  4081  iunxun  4412  oarec  7230  zornn0g  8906  scshwfzeqfzo  12794  rpnnen2  13959  vdwlem6  14504  pmatcollpw3fi1  19289  cmpfi  19908  unima  31441
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-v 3111  df-un 3480
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