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Theorem unss1 3142
 Description: Subclass law for union of classes. (Contributed by NM, 14-Oct-1999.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
unss1

Proof of Theorem unss1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssel 2994 . . . 4
21orim1d 734 . . 3
3 elun 3114 . . 3
4 elun 3114 . . 3
52, 3, 43imtr4g 203 . 2
65ssrdv 3006 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 662   wcel 1434   cun 2972   wss 2974 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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-in 2980  df-ss 2987 This theorem is referenced by:  unss2  3144  unss12  3145  undif1ss  3325  eldifpw  4234  tposss  5895  dftpos4  5912
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