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Theorem iunss1 4096
 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 3400 . . 3
2 eliun 4089 . . 3
3 eliun 4089 . . 3
41, 2, 33imtr4g 262 . 2
54ssrdv 3346 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1725  wrex 2698   wss 3312  ciun 4085 This theorem is referenced by:  iuneq1  4098  iunxdif2  4131  oelim2  6830  fsumiun  12592  ovolfiniun  19389  uniioovol  19463  volsupnfl  26241  usgreghash2spotv  28392  bnj1413  29341  bnj1408  29342 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-v 2950  df-in 3319  df-ss 3326  df-iun 4087
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