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Theorem dfiun2g 3877
 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
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfra1 2485 . . . . . 6
2 rsp 2501 . . . . . . . 8
3 clel3g 2843 . . . . . . . 8
42, 3syl6 33 . . . . . . 7
54imp 123 . . . . . 6
61, 5rexbida 2449 . . . . 5
7 rexcom4 2732 . . . . 5
86, 7bitrdi 195 . . . 4
9 r19.41v 2610 . . . . . 6
109exbii 1582 . . . . 5
11 exancom 1585 . . . . 5
1210, 11bitri 183 . . . 4
138, 12bitrdi 195 . . 3
14 eliun 3849 . . 3
15 eluniab 3780 . . 3
1613, 14, 153bitr4g 222 . 2
1716eqrdv 2152 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1332  wex 1469   wcel 2125  cab 2140  wral 2432  wrex 2433  cuni 3768  ciun 3845 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-ral 2437  df-rex 2438  df-v 2711  df-uni 3769  df-iun 3847 This theorem is referenced by:  dfiun2  3879  abnexg  4400  dfiun3g  4836  fniunfv  5703  iunexg  6057  uniqs  6527  iunopn  12339
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