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Theorem sucid 4103
 Description: A set belongs to its successor. (Contributed by NM, 22-Jun-1994.) (Proof shortened by Alan Sare, 18-Feb-2012.) (Proof shortened by Scott Fenton, 20-Feb-2012.)
Hypothesis
Ref Expression
sucid.1 A V
Assertion
Ref Expression
sucid A suc A

Proof of Theorem sucid
StepHypRef Expression
1 sucid.1 . 2 A V
2 sucidg 4102 . 2 (A V → A suc A)
31, 2ax-mp 7 1 A suc A
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1374  Vcvv 2535  suc csuc 4051 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004 This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-un 2899  df-sn 3356  df-suc 4057 This theorem is referenced by:  eqelsuc  4105  unon  4186  ordunisuc2r  4189  ordsoexmid  4224  limom  4263  0elnn  4267  tfrexlem  5870  prarloclemarch2  6276  prarloclemlt  6347  bj-nn0suc0  7172  bj-nnelirr  7175  bj-inf2vnlem2  7189  bj-findis  7197
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