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Theorem iunss2 3781
 Description: A subclass condition on the members of two indexed classes and that implies a subclass relation on their indexed unions. Generalization of Proposition 8.6 of [TakeutiZaring] p. 59. Compare uniss2 3690. (Contributed by NM, 9-Dec-2004.)
Assertion
Ref Expression
iunss2
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()   ()

Proof of Theorem iunss2
StepHypRef Expression
1 ssiun 3778 . . 3
21ralimi 2439 . 2
3 iunss 3777 . 2
42, 3sylibr 133 1
 Colors of variables: wff set class Syntax hints:   wi 4  wral 2360  wrex 2361   wss 3000  ciun 3736 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 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-ral 2365  df-rex 2366  df-v 2622  df-in 3006  df-ss 3013  df-iun 3738 This theorem is referenced by:  iunxdif2  3784  rdgss  6162
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