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Theorem sseldi 2943
Description: Membership inference from subclass relationship. (Contributed by NM, 25-Jun-2014.)
Hypotheses
Ref Expression
sseli.1 𝐴𝐵
sseldi.2 (𝜑𝐶𝐴)
Assertion
Ref Expression
sseldi (𝜑𝐶𝐵)

Proof of Theorem sseldi
StepHypRef Expression
1 sseldi.2 . 2 (𝜑𝐶𝐴)
2 sseli.1 . . 3 𝐴𝐵
32sseli 2941 . 2 (𝐶𝐴𝐶𝐵)
41, 3syl 14 1 (𝜑𝐶𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1393  wss 2917
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 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-ss 2931
This theorem is referenced by:  riotacl  5482  riotasbc  5483  elmpt2cl  5698  ofrval  5722  mpt2xopn0yelv  5854  tpostpos  5879  smores  5907  prarloclemcalc  6598  rereceu  6961  recriota  6962  rexrd  7073  nnred  7925  nncnd  7926  un0addcl  8213  un0mulcl  8214  nnnn0d  8233  nn0red  8234  nn0zd  8356  zred  8358  rpred  8620  ige2m1fz  8970  iseqcaopr2  9215  expcl2lemap  9241  m1expcl  9252
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