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Theorem iunss1 4343
 Description: Subclass theorem for indexed union. (Contributed by NM, 10-Dec-2004.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
iunss1
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem iunss1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssrexv 3570 . . 3
2 eliun 4336 . . 3
3 eliun 4336 . . 3
41, 2, 33imtr4g 270 . 2
54ssrdv 3515 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wcel 1767  wrex 2818   wss 3481  ciun 4331 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2822  df-rex 2823  df-v 3120  df-in 3488  df-ss 3495  df-iun 4333 This theorem is referenced by:  iuneq1  4345  iunxdif2  4379  oelim2  7256  fsumiun  13615  ovolfiniun  21780  uniioovol  21856  usgreghash2spotv  24881  volsupnfl  29977  bnj1413  33526  bnj1408  33527
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