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Theorem elunirab 4028
 Description: Membership in union of a class abstraction. (Contributed by NM, 4-Oct-2006.)
Assertion
Ref Expression
elunirab
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem elunirab
StepHypRef Expression
1 eluniab 4027 . 2
2 df-rab 2714 . . . 4
32unieqi 4025 . . 3
43eleq2i 2500 . 2
5 df-rex 2711 . . 3
6 an12 773 . . . 4
76exbii 1592 . . 3
85, 7bitri 241 . 2
91, 4, 83bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wex 1550   wcel 1725  cab 2422  wrex 2706  crab 2709  cuni 4015 This theorem is referenced by:  neiptopuni  17194  cmpcov2  17453  tgcmp  17464  hauscmplem  17469  concompid  17494  alexsubALT  18082  cvmliftlem15  24985  fnessref  26373  cover2  26415 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 2711  df-rab 2714  df-v 2958  df-uni 4016
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