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Theorem sucel 4956
 Description: Membership of a successor in another class. (Contributed by NM, 29-Jun-2004.)
Assertion
Ref Expression
sucel
Distinct variable groups:   ,,   ,

Proof of Theorem sucel
StepHypRef Expression
1 risset 2982 . 2
2 dfcleq 2450 . . . 4
3 vex 3112 . . . . . . 7
43elsuc 4952 . . . . . 6
54bibi2i 313 . . . . 5
65albii 1640 . . . 4
72, 6bitri 249 . . 3
87rexbii 2959 . 2
91, 8bitri 249 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  \/wo 368  A.wal 1393  =wceq 1395  e.wcel 1818  E.wrex 2808  succsuc 4885 This theorem is referenced by:  axinf2  8078  zfinf2  8080 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-v 3111  df-un 3480  df-sn 4030  df-suc 4889
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