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Theorem sseldd 3015
Description: Membership inference from subclass relationship. (Contributed by NM, 14-Dec-2004.)
Hypotheses
Ref Expression
sseld.1 (𝜑𝐴𝐵)
sseldd.2 (𝜑𝐶𝐴)
Assertion
Ref Expression
sseldd (𝜑𝐶𝐵)

Proof of Theorem sseldd
StepHypRef Expression
1 sseldd.2 . 2 (𝜑𝐶𝐴)
2 sseld.1 . . 3 (𝜑𝐴𝐵)
32sseld 3013 . 2 (𝜑 → (𝐶𝐴𝐶𝐵))
41, 3mpd 13 1 (𝜑𝐶𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1436  wss 2988
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-11 1440  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-in 2994  df-ss 3001
This theorem is referenced by:  exmid01  4008  frirrg  4153  ordtri2or2exmid  4362  riotass  5598  tfrcldm  6084  eroveu  6337  eroprf  6339  findcard2d  6561  findcard2sd  6562  fimax2gtrilemstep  6570  undifdc  6588  fisseneq  6595  suplub2ti  6643  nnppipi  6849  archnqq  6923  prarloclemlt  6999  suprubex  8350  suprzclex  8780  fzssp1  9415  elfzoelz  9489  fzofzp1  9569  fzostep1  9579  frecuzrdgg  9754  frecuzrdgdomlem  9755  frecuzrdgsuctlem  9761  iseqvalt  9804  isermono  9831  bcm1k  10086  fimaxq  10153  leisorel  10160  zfz1isolemiso  10162  iseqcoll  10165  fimaxre2  10574  isummolem2a  10684  fisumcvg3  10698  fsumcl2lem  10699  zssinfcl  10869
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