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Theorem sselii 2970
Description: Membership inference from subclass relationship. (Contributed by NM, 31-May-1999.)
Hypotheses
Ref Expression
sseli.1 𝐴𝐵
sselii.2 𝐶𝐴
Assertion
Ref Expression
sselii 𝐶𝐵

Proof of Theorem sselii
StepHypRef Expression
1 sselii.2 . 2 𝐶𝐴
2 sseli.1 . . 3 𝐴𝐵
32sseli 2969 . 2 (𝐶𝐴𝐶𝐵)
41, 3ax-mp 7 1 𝐶𝐵
Colors of variables: wff set class
Syntax hints:  wcel 1409  wss 2945
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-in 2952  df-ss 2959
This theorem is referenced by:  brtpos0  5898  ax1cn  6995  recni  7097  0xr  7131  nn0rei  8250  nnzi  8323  nn0zi  8324  pnfxr  8793
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