MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  unss1 Unicode version

Theorem unss1 3672
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 3497 . . . 4
21orim1d 839 . . 3
3 elun 3644 . . 3
4 elun 3644 . . 3
52, 3, 43imtr4g 270 . 2
65ssrdv 3509 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  \/wo 368  e.wcel 1818  u.cun 3473  C_wss 3475
This theorem is referenced by:  unss2  3674  unss12  3675  eldifpw  6612  tposss  6975  dftpos4  6993  hashbclem  12501  incexclem  13648  mreexexlem2d  15042  catcoppccl  15435  neitr  19681  restntr  19683  leordtval2  19713  cmpcld  19902  uniioombllem3  21994  limcres  22290  plyss  22596  shlej1  26278  ss2mcls  28928  orderseqlem  29332  bj-rrhatsscchat  34639  pclfinclN  35674
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480  df-in 3482  df-ss 3489
  Copyright terms: Public domain W3C validator