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Theorem elun1 3153
Description: Membership law for union of classes. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
elun1 (𝐴𝐵𝐴 ∈ (𝐵𝐶))

Proof of Theorem elun1
StepHypRef Expression
1 ssun1 3149 . 2 𝐵 ⊆ (𝐵𝐶)
21sseli 3008 1 (𝐴𝐵𝐴 ∈ (𝐵𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1436  cun 2984
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2616  df-un 2990  df-in 2992  df-ss 2999
This theorem is referenced by:  exmidundif  4002  brtposg  5954  dftpos4  5963  dcdifsnid  6198  undifdcss  6563  djulclr  6662  djulcl  6664  djuss  6682  finomni  6717  hashennnuni  10036
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