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Theorem elsuci 4949
Description: Membership in a successor. This one-way implication does not require that either or be sets. (Contributed by NM, 6-Jun-1994.)
Assertion
Ref Expression
elsuci

Proof of Theorem elsuci
StepHypRef Expression
1 df-suc 4889 . . . 4
21eleq2i 2535 . . 3
3 elun 3644 . . 3
42, 3bitri 249 . 2
5 elsni 4054 . . 3
65orim2i 518 . 2
74, 6sylbi 195 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  \/wo 368  =wceq 1395  e.wcel 1818  u.cun 3473  {csn 4029  succsuc 4885
This theorem is referenced by:  trsucss  4968  ordnbtwn  4973  suc11  4986  tfrlem11  7076  omordi  7234  nnmordi  7299  phplem3  7718  pssnn  7758  r1sdom  8213  cfsuc  8658  axdc3lem2  8852  axdc3lem4  8854  indpi  9306  ontgval  29896  onsucconi  29902  suctrALT  33626  suctrALT2VD  33636  suctrALT2  33637  suctrALTcf  33722  suctrALTcfVD  33723  suctrALT3  33724  bnj563  33800  bnj964  34001
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-v 3111  df-un 3480  df-sn 4030  df-suc 4889
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