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Theorem sucel 4096
 Description: Membership of a successor in another class. (Contributed by NM, 29-Jun-2004.)
Assertion
Ref Expression
sucel
Distinct variable groups:   ,,   ,
Allowed substitution hint:   ()

Proof of Theorem sucel
StepHypRef Expression
1 risset 2330 . 2
2 dfcleq 2016 . . . 4
3 vex 2538 . . . . . . 7
43elsuc 4092 . . . . . 6
54bibi2i 216 . . . . 5
65albii 1339 . . . 4
72, 6bitri 173 . . 3
87rexbii 2309 . 2
91, 8bitri 173 1
 Colors of variables: wff set class Syntax hints:   wb 98   wo 616  wal 1226   wceq 1228   wcel 1374  wrex 2285   csuc 4051 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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004 This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-rex 2290  df-v 2537  df-un 2899  df-sn 3356  df-suc 4057 This theorem is referenced by: (None)
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