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Theorem sseldd 2940
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 2938 . 2 (φ → (𝐶 A𝐶 B))
41, 3mpd 13 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:  riotass  5438  eroveu  6133  eroprf  6135  nnppipi  6327  archnqq  6400  prarloclemlt  6475  fzssp1  8660  elfzoelz  8734  fzofzp1  8813  fzostep1  8823
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