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Theorem dfiun2g 3833
 Description: Alternate definition of indexed union when is a set. Definition 15(a) of [Suppes] p. 44. (Contributed by NM, 23-Mar-2006.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
dfiun2g
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()   (,)

Proof of Theorem dfiun2g
StepHypRef Expression
1 nfra1 2555 . . . . . 6
2 ra4 2565 . . . . . . . 8
3 clel3g 2842 . . . . . . . 8
42, 3syl6 31 . . . . . . 7
54imp 420 . . . . . 6
61, 5rexbida 2522 . . . . 5
7 rexcom4 2745 . . . . 5
86, 7syl6bb 254 . . . 4
9 r19.41v 2655 . . . . . 6
109exbii 1580 . . . . 5
11 exancom 1584 . . . . 5
1210, 11bitri 242 . . . 4
138, 12syl6bb 254 . . 3
14 eliun 3807 . . 3
15 eluniab 3739 . . 3
1613, 14, 153bitr4g 281 . 2
1716eqrdv 2251 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wex 1537   wceq 1619   wcel 1621  cab 2239  wral 2509  wrex 2510  cuni 3727  ciun 3803 This theorem is referenced by:  dfiun2  3835  dfiun3g  4838  iunexg  5619  uniqs  6605  ac6num  7990  iunopn  16476  pnrmopn  16903  cncmp  16951  ptcmplem3  17580  iunmbl  18742  voliun  18743 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-uni 3728  df-iun 3805
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