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Theorem elsuc2g 4951
Description: Variant of membership in a successor, requiring that rather than be a set. (Contributed by NM, 28-Oct-2003.)
Assertion
Ref Expression
elsuc2g

Proof of Theorem elsuc2g
StepHypRef Expression
1 df-suc 4889 . . 3
21eleq2i 2535 . 2
3 elun 3644 . . 3
4 elsnc2g 4059 . . . 4
54orbi2d 701 . . 3
63, 5syl5bb 257 . 2
72, 6syl5bb 257 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  \/wo 368  =wceq 1395  e.wcel 1818  u.cun 3473  {csn 4029  succsuc 4885
This theorem is referenced by:  elsuc2  4953  om2uzlti  12061
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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