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Theorem elun1 3137
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 3133 . 2 𝐵 ⊆ (𝐵𝐶)
21sseli 2968 1 (𝐴𝐵𝐴 ∈ (𝐵𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1409  cun 2942
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-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  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-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2949  df-in 2951  df-ss 2958
This theorem is referenced by:  brtposg  5899  dftpos4  5908  nndifsnid  6110  fidifsnid  6362
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