Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  unimax Structured version   Unicode version

Theorem unimax 4274
 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
Distinct variable groups:   ,   ,

Proof of Theorem unimax
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssid 3516 . . 3
2 sseq1 3518 . . . 4
32elrab3 3255 . . 3
41, 3mpbiri 233 . 2
5 sseq1 3518 . . . . 5
65elrab 3254 . . . 4
76simprbi 464 . . 3
87rgen 2817 . 2
9 ssunieq 4273 . . 3
109eqcomd 2468 . 2
114, 8, 10sylancl 662 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1374   wcel 1762  wral 2807  crab 2811   wss 3469  cuni 4238 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-ral 2812  df-rab 2816  df-v 3108  df-in 3476  df-ss 3483  df-uni 4239 This theorem is referenced by:  lssuni  17362  chsupid  25992  shatomistici  26942  lssats  33684  lpssat  33685  lssatle  33687  lssat  33688
 Copyright terms: Public domain W3C validator