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Theorem sselii 3098
Description: Membership inference from subclass relationship. (Contributed by NM, 31-May-1999.)
Hypotheses
Ref Expression
sseli.1  |-  A  C_  B
sselii.2  |-  C  e.  A
Assertion
Ref Expression
sselii  |-  C  e.  B

Proof of Theorem sselii
StepHypRef Expression
1 sselii.2 . 2  |-  C  e.  A
2 sseli.1 . . 3  |-  A  C_  B
32sseli 3097 . 2  |-  ( C  e.  A  ->  C  e.  B )
41, 3ax-mp 5 1  |-  C  e.  B
Colors of variables: wff set class
Syntax hints:    e. wcel 1481    C_ wss 3075
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-in 3081  df-ss 3088
This theorem is referenced by:  brtpos0  6156  ax1cn  7692  recni  7801  0xr  7835  pnfxr  7841  nn0rei  9011  0xnn0  9069  nnzi  9098  nn0zi  9099
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