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Theorem uniss2 4245
 Description: A subclass condition on the members of two classes that implies a subclass relation on their unions. Proposition 8.6 of [TakeutiZaring] p. 59. See iunss2 4338 for a generalization to indexed unions. (Contributed by NM, 22-Mar-2004.)
Assertion
Ref Expression
uniss2
Distinct variable groups:   ,   ,,
Allowed substitution hint:   ()

Proof of Theorem uniss2
StepHypRef Expression
1 ssuni 4235 . . . . 5
21expcom 436 . . . 4
32rexlimiv 2909 . . 3
43ralimi 2816 . 2
5 unissb 4244 . 2
64, 5sylibr 215 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wcel 1867  wral 2773  wrex 2774   wss 3433  cuni 4213 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ral 2778  df-rex 2779  df-v 3080  df-in 3440  df-ss 3447  df-uni 4214 This theorem is referenced by:  unidif  4246  coflim  8680
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