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Theorem sucid 4120
 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
Assertion
Ref Expression
sucid

Proof of Theorem sucid
StepHypRef Expression
1 sucid.1 . 2
2 sucidg 4119 . 2
31, 2ax-mp 7 1
 Colors of variables: wff set class Syntax hints:   wcel 1390  cvv 2551   csuc 4068 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-sn 3373  df-suc 4074 This theorem is referenced by:  eqelsuc  4122  unon  4202  ordunisuc2r  4205  ordsoexmid  4240  limom  4279  0elnn  4283  tfrexlem  5889  prarloclemarch2  6402  prarloclemlt  6476  bj-nn0suc0  9408  bj-nnelirr  9411  bj-inf2vnlem2  9425  bj-findis  9433
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