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Theorem sseld 2938
Description: Membership deduction from subclass relationship. (Contributed by NM, 15-Nov-1995.)
Hypothesis
Ref Expression
sseld.1  C_
Assertion
Ref Expression
sseld  C  C

Proof of Theorem sseld
StepHypRef Expression
1 sseld.1 . 2  C_
2 ssel 2933 . 2 
C_  C  C
31, 2syl 14 1  C  C
Colors of variables: wff set class
Syntax hints:   wi 4   wcel 1390    C_ wss 2911
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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  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-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925
This theorem is referenced by:  sselda  2939  sseldd  2940  ssneld  2941  elelpwi  3362  ssbrd  3796  uniopel  3984  sucprcreg  4227  ordsuc  4241  0elnn  4283  dmrnssfld  4538  nfunv  4876  opelf  5005  fvimacnv  5225  ffvelrn  5243  f1imass  5356  dftpos3  5818  nnmordi  6025  prarloclemarch2  6402  ltexprlemrl  6584  cauappcvgprlemladdrl  6629  caucvgprlemladdrl  6649  caucvgprlem1  6650  uzind  8125  ixxssxr  8539  elfz0add  8749  elfz0addOLD  8750  fzoss1  8797  bj-nnord  9418
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