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Theorem sseldi 2937
Description: Membership inference from subclass relationship. (Contributed by NM, 25-Jun-2014.)
Hypotheses
Ref Expression
sseli.1 AB
sseldi.2 (φ𝐶 A)
Assertion
Ref Expression
sseldi (φ𝐶 B)

Proof of Theorem sseldi
StepHypRef Expression
1 sseldi.2 . 2 (φ𝐶 A)
2 sseli.1 . . 3 AB
32sseli 2935 . 2 (𝐶 A𝐶 B)
41, 3syl 14 1 (φ𝐶 B)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1390  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:  riotacl  5425  riotasbc  5426  elmpt2cl  5640  ofrval  5664  mpt2xopn0yelv  5795  tpostpos  5820  smores  5848  prarloclemcalc  6484  rexrd  6832  nnred  7668  nncnd  7669  un0addcl  7951  un0mulcl  7952  nnnn0d  7971  nn0red  7972  nn0zd  8094  zred  8096  rpred  8357  ige2m1fz  8702  expcl2lemap  8881  m1expcl  8892
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