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Theorem elsuc 4643
 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 4641 . 2
31, 2ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wb 177   wo 358   wceq 1652   wcel 1725  cvv 2949   csuc 4576 This theorem is referenced by:  sucel  4647  suctrALT  4657  limsssuc  4823  omsmolem  6889  cantnfle  7619  infxpenlem  7888  inatsk  8646  untsucf  25152  dfon2lem7  25409 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2951  df-un 3318  df-sn 3813  df-suc 4580
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