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Theorem iundif2 3867
 Description: Indexed union of class difference. Generalization of half of theorem "De Morgan's laws" in [Enderton] p. 31. Use intiin 3854 to recover Enderton's theorem. (Contributed by NM, 19-Aug-2004.)
Assertion
Ref Expression
iundif2
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem iundif2
StepHypRef Expression
1 eldif 3088 . . . . 5
21rexbii 2532 . . . 4
3 r19.42v 2656 . . . 4
4 rexnal 2518 . . . . . 6
5 vex 2730 . . . . . . 7
6 eliin 3808 . . . . . . 7
75, 6ax-mp 10 . . . . . 6
84, 7xchbinxr 304 . . . . 5
98anbi2i 678 . . . 4
102, 3, 93bitri 264 . . 3
11 eliun 3807 . . 3
12 eldif 3088 . . 3
1310, 11, 123bitr4i 270 . 2
1413eqriv 2250 1
 Colors of variables: wff set class Syntax hints:   wn 5   wb 178   wa 360   wceq 1619   wcel 1621  wral 2509  wrex 2510  cvv 2727   cdif 3075  ciun 3803  ciin 3804 This theorem is referenced by:  iuncld  16614  pnrmopn  16903  alexsublem  17570  bcth3  18585 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-dif 3081  df-iun 3805  df-iin 3806
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