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Theorem unimax 3605
Description: Any member of a class is the largest of those members that it includes. (Contributed by NM, 13-Aug-2002.)
Assertion
Ref Expression
unimax  U. {  |  C_  }
Distinct variable groups:   ,   ,

Proof of Theorem unimax
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssid 2958 . . 3  C_
2 sseq1 2960 . . . 4  C_  C_
32elrab3 2693 . . 3  {  |  C_  }  C_
41, 3mpbiri 157 . 2  {  |  C_  }
5 sseq1 2960 . . . . 5  C_  C_
65elrab 2692 . . . 4  {  |  C_  }  C_
76simprbi 260 . . 3  {  |  C_  }  C_
87rgen 2368 . 2  {  |  C_  }  C_
9 ssunieq 3604 . . 3  {  |  C_  }  {  |  C_  }  C_  U. {  |  C_  }
109eqcomd 2042 . 2  {  |  C_  }  {  |  C_  }  C_  U. {  |  C_  }
114, 8, 10sylancl 392 1  U. {  |  C_  }
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wceq 1242   wcel 1390  wral 2300   {crab 2304    C_ wss 2911   U.cuni 3571
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rab 2309  df-v 2553  df-in 2918  df-ss 2925  df-uni 3572
This theorem is referenced by:  onuniss2  4203
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