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Theorem eluniab 3903
 Description: Membership in union of a class abstraction. (Contributed by NM, 11-Aug-1994.) (Revised by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
eluniab
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem eluniab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eluni 3894 . 2
2 nfv 1619 . . . 4
3 nfsab1 2343 . . . 4
42, 3nfan 1824 . . 3
5 nfv 1619 . . 3
6 eleq2 2414 . . . 4
7 eleq1 2413 . . . . 5
8 abid 2341 . . . . 5
97, 8syl6bb 252 . . . 4
106, 9anbi12d 691 . . 3
114, 5, 10cbvex 1985 . 2
121, 11bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358  wex 1541   wceq 1642   wcel 1710  cab 2339  cuni 3891 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-uni 3892 This theorem is referenced by:  elunirab  3904  dfiun2g  3999  eqtfinrelk  4486  elfv  5326  funiunfv  5467  tcfnex  6244
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