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Theorem ssel2 2934
Description: Membership relationships follow from a subclass relationship. (Contributed by NM, 7-Jun-2004.)
Assertion
Ref Expression
ssel2 ((AB 𝐶 A) → 𝐶 B)

Proof of Theorem ssel2
StepHypRef Expression
1 ssel 2933 . 2 (AB → (𝐶 A𝐶 B))
21imp 115 1 ((AB 𝐶 A) → 𝐶 B)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   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:  elnn  4271  funimass4  5167  fvelimab  5172  ssimaex  5177  funconstss  5228  rexima  5337  ralima  5338  1st2nd  5749  f1o2ndf1  5791  lbzbi  8327  elfzom1elp1fzo  8828  ssfzo12  8850
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