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Theorem elunirab 3988
 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 3987 . 2
2 df-rab 2675 . . . 4
32unieqi 3985 . . 3
43eleq2i 2468 . 2
5 df-rex 2672 . . 3
6 an12 773 . . . 4
76exbii 1589 . . 3
85, 7bitri 241 . 2
91, 4, 83bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wex 1547   wcel 1721  cab 2390  wrex 2667  crab 2670  cuni 3975 This theorem is referenced by:  neiptopuni  17149  cmpcov2  17407  tgcmp  17418  hauscmplem  17423  concompid  17447  alexsubALT  18035  cvmliftlem15  24938  fnessref  26263  cover2  26305 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-rex 2672  df-rab 2675  df-v 2918  df-uni 3976
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