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Theorem elsuc 4952
 Description: Membership in a successor. Exercise 5 of [TakeutiZaring] p. 17. (Contributed by NM, 15-Sep-2003.)
Hypothesis
Ref Expression
elsuc.1
Assertion
Ref Expression
elsuc

Proof of Theorem elsuc
StepHypRef Expression
1 elsuc.1 . 2
2 elsucg 4950 . 2
31, 2ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  \/wo 368  =wceq 1395  e.wcel 1818   cvv 3109  succsuc 4885 This theorem is referenced by:  sucel  4956  suctr  4966  limsssuc  6685  omsmolem  7321  cantnfle  8111  cantnfleOLD  8141  infxpenlem  8412  inatsk  9177  untsucf  29082  dfon2lem7  29221 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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