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Theorem elssuni 3764
 Description: An element of a class is a subclass of its union. Theorem 8.6 of [Quine] p. 54. Also the basis for Proposition 7.20 of [TakeutiZaring] p. 40. (Contributed by NM, 6-Jun-1994.)
Assertion
Ref Expression
elssuni

Proof of Theorem elssuni
StepHypRef Expression
1 ssid 3117 . 2
2 ssuni 3758 . 2
31, 2mpan 420 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1480   wss 3071  cuni 3736 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-in 3077  df-ss 3084  df-uni 3737 This theorem is referenced by:  unissel  3765  ssunieq  3769  pwuni  4116  pwel  4140  uniopel  4178  iunpw  4401  dmrnssfld  4802  fvssunirng  5436  relfvssunirn  5437  sefvex  5442  riotaexg  5734  pwuninel2  6179  tfrlem9  6216  tfrexlem  6231  sbthlem1  6845  sbthlem2  6846  unirnioo  9756  eltopss  12176  toponss  12193  isbasis3g  12213  baspartn  12217  bastg  12230  tgcl  12233  epttop  12259  difopn  12277  ssntr  12291  isopn3  12294  isopn3i  12304  neiuni  12330  resttopon  12340  restopn2  12352  ssidcn  12379  lmtopcnp  12419  txuni2  12425  hmeoimaf1o  12483  tgioo  12715  bj-elssuniab  12998
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