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Theorem uniss2 3756
 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 3845 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 3749 . . . . 5
21expcom 426 . . . 4
32rexlimiv 2623 . . 3
43ralimi 2580 . 2
5 unissb 3755 . 2
64, 5sylibr 205 1
 Colors of variables: wff set class Syntax hints:   wi 6   wcel 1621  wral 2509  wrex 2510   wss 3078  cuni 3727 This theorem is referenced by:  unidif  3757  coflim  7771  unint2t  24684  intfmu2  24685 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ral 2513  df-rex 2514  df-v 2729  df-in 3085  df-ss 3089  df-uni 3728
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