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Theorem sselii 2936
Description: Membership inference from subclass relationship. (Contributed by NM, 31-May-1999.)
Hypotheses
Ref Expression
sseli.1  C_
sselii.2  C
Assertion
Ref Expression
sselii  C

Proof of Theorem sselii
StepHypRef Expression
1 sselii.2 . 2  C
2 sseli.1 . . 3  C_
32sseli 2935 . 2  C  C
41, 3ax-mp 7 1  C
Colors of variables: wff set class
Syntax hints:   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:  brtpos0  5808  ax1cn  6747  recni  6837  0xr  6869  nn0rei  7968  nnzi  8042  nn0zi  8043  pnfxr  8462
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