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Theorem sucel 4113
Description: Membership of a successor in another class. (Contributed by NM, 29-Jun-2004.)
Assertion
Ref Expression
sucel  suc
Distinct variable groups:   ,,   ,
Allowed substitution hint:   ()

Proof of Theorem sucel
StepHypRef Expression
1 risset 2346 . 2  suc  suc
2 dfcleq 2031 . . . 4  suc  suc
3 vex 2554 . . . . . . 7 
_V
43elsuc 4109 . . . . . 6  suc
54bibi2i 216 . . . . 5 
suc
65albii 1356 . . . 4  suc
72, 6bitri 173 . . 3  suc
87rexbii 2325 . 2  suc
91, 8bitri 173 1  suc
Colors of variables: wff set class
Syntax hints:   wb 98   wo 628  wal 1240   wceq 1242   wcel 1390  wrex 2301   suc csuc 4068
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-un 2916  df-sn 3373  df-suc 4074
This theorem is referenced by: (None)
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