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Theorem unimax 3925
 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 3290 . . 3
2 sseq1 3292 . . . 4
32elrab3 2995 . . 3
41, 3mpbiri 224 . 2
5 sseq1 3292 . . . . 5
65elrab 2994 . . . 4
76simprbi 450 . . 3
87rgen 2679 . 2
9 ssunieq 3924 . . 3
109eqcomd 2358 . 2
114, 8, 10sylancl 643 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358   wceq 1642   wcel 1710  wral 2614  crab 2618   wss 3257  cuni 3891 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rab 2623  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-uni 3892 This theorem is referenced by: (None)
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