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Theorem ssel2 2968
Description: Membership relationships follow from a subclass relationship. (Contributed by NM, 7-Jun-2004.)
Assertion
Ref Expression
ssel2 ((𝐴𝐵𝐶𝐴) → 𝐶𝐵)

Proof of Theorem ssel2
StepHypRef Expression
1 ssel 2967 . 2 (𝐴𝐵 → (𝐶𝐴𝐶𝐵))
21imp 119 1 ((𝐴𝐵𝐶𝐴) → 𝐶𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  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:  elnn  4356  funimass4  5252  fvelimab  5257  ssimaex  5262  funconstss  5313  rexima  5422  ralima  5423  1st2nd  5835  f1o2ndf1  5877  lbzbi  8648  elfzom1elp1fzo  9160  ssfzo12  9182  iseqsplit  9402  shftlem  9645
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