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Theorem uniss2 3858
 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 3947 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 3849 . . . . 5
21expcom 424 . . . 4
32rexlimiv 2661 . . 3
43ralimi 2618 . 2
5 unissb 3857 . 2
64, 5sylibr 203 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1684  wral 2543  wrex 2544   wss 3152  cuni 3827 This theorem is referenced by:  unidif  3859  coflim  7887  unint2t  25518  intfmu2  25519 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-v 2790  df-in 3159  df-ss 3166  df-uni 3828
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