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Theorem eqelsuc 4184
 Description: A set belongs to the successor of an equal set. (Contributed by NM, 18-Aug-1994.)
Hypothesis
Ref Expression
eqelsuc.1
Assertion
Ref Expression
eqelsuc

Proof of Theorem eqelsuc
StepHypRef Expression
1 eqelsuc.1 . . 3
21sucid 4182 . 2
3 suceq 4167 . 2
42, 3syl5eleq 2142 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1259   wcel 1409  cvv 2574   csuc 4130 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-sn 3409  df-suc 4136 This theorem is referenced by: (None)
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