ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  elun2 GIF version

Theorem elun2 3244
Description: Membership law for union of classes. (Contributed by NM, 30-Aug-1993.)
Assertion
Ref Expression
elun2 (𝐴𝐵𝐴 ∈ (𝐶𝐵))

Proof of Theorem elun2
StepHypRef Expression
1 ssun2 3240 . 2 𝐵 ⊆ (𝐶𝐵)
21sseli 3093 1 (𝐴𝐵𝐴 ∈ (𝐶𝐵))
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1480  cun 3069
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084
This theorem is referenced by:  dcun  3473  exmidundif  4129  exmidundifim  4130  dftpos4  6160  tfrlemibxssdm  6224  tfrlemi14d  6230  tfr1onlembxssdm  6240  tfr1onlemres  6246  tfrcllembxssdm  6253  tfrcllemres  6259  dcdifsnid  6400  findcard2d  6785  findcard2sd  6786  onunsnss  6805  undifdcss  6811  fisseneq  6820  fidcenumlemrks  6841  djurclr  6935  djurcl  6937  djuss  6955  finomni  7012  mnfxr  7834  hashinfuni  10535  fsumsplitsnun  11200  sumsplitdc  11213  modfsummodlem1  11237  exmidunben  11950  srnginvld  12099  lmodvscad  12110  ipsscad  12118  ipsvscad  12119  ipsipd  12120
  Copyright terms: Public domain W3C validator