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Theorem ss2iun 3775
 Description: Subclass theorem for indexed union. (Contributed by NM, 26-Nov-2003.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
ss2iun

Proof of Theorem ss2iun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssel 3041 . . . . 5
21ralimi 2454 . . . 4
3 rexim 2485 . . . 4
42, 3syl 14 . . 3
5 eliun 3764 . . 3
6 eliun 3764 . . 3
74, 5, 63imtr4g 204 . 2
87ssrdv 3053 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1448  wral 2375  wrex 2376   wss 3021  ciun 3760 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082 This theorem depends on definitions:  df-bi 116  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-ral 2380  df-rex 2381  df-v 2643  df-in 3027  df-ss 3034  df-iun 3762 This theorem is referenced by:  iuneq2  3776  abnexg  4305  dvfvalap  12523
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