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Theorem sseld 3022
Description: Membership deduction from subclass relationship. (Contributed by NM, 15-Nov-1995.)
Hypothesis
Ref Expression
sseld.1  |-  ( ph  ->  A  C_  B )
Assertion
Ref Expression
sseld  |-  ( ph  ->  ( C  e.  A  ->  C  e.  B ) )

Proof of Theorem sseld
StepHypRef Expression
1 sseld.1 . 2  |-  ( ph  ->  A  C_  B )
2 ssel 3017 . 2  |-  ( A 
C_  B  ->  ( C  e.  A  ->  C  e.  B ) )
31, 2syl 14 1  |-  ( ph  ->  ( C  e.  A  ->  C  e.  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1438    C_ wss 2997
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-in 3003  df-ss 3010
This theorem is referenced by:  sselda  3023  sseldd  3024  ssneld  3025  elelpwi  3436  ssbrd  3878  uniopel  4074  onintonm  4324  sucprcreg  4355  ordsuc  4369  0elnn  4422  dmrnssfld  4684  nfunv  5033  opelf  5167  fvimacnv  5398  ffvelrn  5416  resflem  5446  f1imass  5535  dftpos3  6009  nnmordi  6255  mapsn  6427  diffifi  6590  ordiso2  6707  prarloclemarch2  6957  ltexprlemrl  7148  cauappcvgprlemladdrl  7195  caucvgprlemladdrl  7216  caucvgprlem1  7217  uzind  8827  supinfneg  9052  infsupneg  9053  ixxssxr  9287  elfz0add  9499  fzoss1  9547  frecuzrdgrclt  9787  fisumcvg  10730  fsum3cvg  10731  isumrpcl  10850  bj-nnord  11510
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