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Theorem unimax 4041
 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 3359 . . 3
2 sseq1 3361 . . . 4
32elrab3 3085 . . 3
41, 3mpbiri 225 . 2
5 sseq1 3361 . . . . 5
65elrab 3084 . . . 4
76simprbi 451 . . 3
87rgen 2763 . 2
9 ssunieq 4040 . . 3
109eqcomd 2440 . 2
114, 8, 10sylancl 644 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  wral 2697  crab 2701   wss 3312  cuni 4007 This theorem is referenced by:  lssuni  16006  chsupid  22904  shatomistici  23854  lssats  29711  lpssat  29712  lssatle  29714  lssat  29715 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rab 2706  df-v 2950  df-in 3319  df-ss 3326  df-uni 4008
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