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Theorem sseldd 2923
Description: Membership inference from subclass relationship. (Contributed by NM, 14-Dec-2004.)
Hypotheses
Ref Expression
sseld.1 (φAB)
sseldd.2 (φ𝐶 A)
Assertion
Ref Expression
sseldd (φ𝐶 B)

Proof of Theorem sseldd
StepHypRef Expression
1 sseldd.2 . 2 (φ𝐶 A)
2 sseld.1 . . 3 (φAB)
32sseld 2921 . 2 (φ → (𝐶 A𝐶 B))
41, 3mpd 13 1 (φ𝐶 B)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1374  wss 2894
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 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-11 1378  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-in 2901  df-ss 2908
This theorem is referenced by:  riotass  5419  eroveu  6108  eroprf  6110  nnppipi  6202  archnqq  6274  prarloclemlt  6347
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