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Theorem elunii 3548
Description: Membership in class union. (Contributed by NM, 24-Mar-1995.)
Assertion
Ref Expression
elunii  C  U. C

Proof of Theorem elunii
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq2 2074 . . . . 5
2 eleq1 2073 . . . . 5  C  C
31, 2anbi12d 442 . . . 4  C  C
43spcegv 2609 . . 3  C  C  C
54anabsi7 500 . 2  C  C
6 eluni 3546 . 2  U. C  C
75, 6sylibr 137 1  C  U. C
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wceq 1223  wex 1354   wcel 1366   U.cuni 3543
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 614  ax-5 1309  ax-7 1310  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-8 1368  ax-10 1369  ax-11 1370  ax-i12 1371  ax-bnd 1372  ax-4 1373  ax-17 1392  ax-i9 1396  ax-ial 1400  ax-i5r 1401  ax-ext 1995
This theorem depends on definitions:  df-bi 110  df-tru 1226  df-nf 1323  df-sb 1619  df-clab 2000  df-cleq 2006  df-clel 2009  df-nfc 2140  df-v 2528  df-uni 3544
This theorem is referenced by:  ssuni  3565  unipw  3916  opeluu  4120  sucunielr  4173  unon  4174  ordunisuc2r  4177  tfrlemibxssdm  5850
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