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Theorem iunss2 4128
 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 4038. (Contributed by NM, 9-Dec-2004.)
Assertion
Ref Expression
iunss2
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()   ()

Proof of Theorem iunss2
StepHypRef Expression
1 ssiun 4125 . . 3
21ralimi 2773 . 2
3 iunss 4124 . 2
42, 3sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wi 4  wral 2697  wrex 2698   wss 3312  ciun 4085 This theorem is referenced by:  iunxdif2  4131  oaass  6795  odi  6813  omass  6814  oelim2  6829 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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