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Theorem rexun 3368
 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 2562 . 2
2 19.43 1595 . . 3
3 elun 3329 . . . . . 6
43anbi1i 676 . . . . 5
5 andir 838 . . . . 5
64, 5bitri 240 . . . 4
76exbii 1572 . . 3
8 df-rex 2562 . . . 4
9 df-rex 2562 . . . 4
108, 9orbi12i 507 . . 3
112, 7, 103bitr4i 268 . 2
121, 11bitri 240 1
 Colors of variables: wff set class Syntax hints:   wb 176   wo 357   wa 358  wex 1531   wcel 1696  wrex 2557   cun 3163 This theorem is referenced by:  rexprg  3696  rextpg  3698  iunxun  3999  oarec  6576  zornn0g  8148  rpnnen2  12520  vdwlem6  13049  cmpfi  17151  rexunOLD  26444 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-v 2803  df-un 3170
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