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Theorem ssel2 2940
 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 2939 . 2 (𝐴𝐵 → (𝐶𝐴𝐶𝐵))
21imp 115 1 ((𝐴𝐵𝐶𝐴) → 𝐶𝐵)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ∈ wcel 1393   ⊆ wss 2917 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 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-ss 2931 This theorem is referenced by:  elnn  4328  funimass4  5224  fvelimab  5229  ssimaex  5234  funconstss  5285  rexima  5394  ralima  5395  1st2nd  5807  f1o2ndf1  5849  lbzbi  8551  elfzom1elp1fzo  9058  ssfzo12  9080  iseqsplit  9238  shftlem  9417
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