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Theorem sucel 4147
 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 2352 . 2
2 dfcleq 2034 . . . 4
3 vex 2560 . . . . . . 7
43elsuc 4143 . . . . . 6
54bibi2i 216 . . . . 5
65albii 1359 . . . 4
72, 6bitri 173 . . 3
87rexbii 2331 . 2
91, 8bitri 173 1
 Colors of variables: wff set class Syntax hints:   wb 98   wo 629  wal 1241   wceq 1243   wcel 1393  wrex 2307   csuc 4102 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-un 2922  df-sn 3381  df-suc 4108 This theorem is referenced by: (None)
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