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Theorem sselda 2945
 Description: Membership deduction from subclass relationship. (Contributed by NM, 26-Jun-2014.)
Hypothesis
Ref Expression
sseld.1 (𝜑𝐴𝐵)
Assertion
Ref Expression
sselda ((𝜑𝐶𝐴) → 𝐶𝐵)

Proof of Theorem sselda
StepHypRef Expression
1 sseld.1 . . 3 (𝜑𝐴𝐵)
21sseld 2944 . 2 (𝜑 → (𝐶𝐴𝐶𝐵))
32imp 115 1 ((𝜑𝐶𝐴) → 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:  elrel  4442  ffvresb  5328  1stdm  5808  tfrlem1  5923  tfrlemiubacc  5944  erinxp  6180  fundmen  6286  ordiso2  6357  elprnql  6579  elprnqu  6580  un0addcl  8215  un0mulcl  8216  icoshftf1o  8859  elfzom1elfzo  9059  zpnn0elfzo  9063  iseqfveq  9230  monoord2  9236
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