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Theorem eqelsuc 4122
Description: A set belongs to the successor of an equal set. (Contributed by NM, 18-Aug-1994.)
Hypothesis
Ref Expression
eqelsuc.1  _V
Assertion
Ref Expression
eqelsuc  suc

Proof of Theorem eqelsuc
StepHypRef Expression
1 eqelsuc.1 . . 3  _V
21sucid 4120 . 2  suc
3 suceq 4105 . 2  suc  suc
42, 3syl5eleq 2123 1  suc
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242   wcel 1390   _Vcvv 2551   suc 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: (None)
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