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Theorem dfiun2g 3689
 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 2355 . . . . . 6
2 rsp 2369 . . . . . . . 8
3 clel3g 2678 . . . . . . . 8
42, 3syl6 29 . . . . . . 7
54imp 115 . . . . . 6
61, 5rexbida 2321 . . . . 5
7 rexcom4 2577 . . . . 5
86, 7syl6bb 185 . . . 4
9 r19.41v 2466 . . . . . 6
109exbii 1496 . . . . 5
11 exancom 1499 . . . . 5
1210, 11bitri 173 . . . 4
138, 12syl6bb 185 . . 3
14 eliun 3661 . . 3
15 eluniab 3592 . . 3
1613, 14, 153bitr4g 212 . 2
1716eqrdv 2038 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1243  wex 1381   wcel 1393  cab 2026  wral 2306  wrex 2307  cuni 3580  ciun 3657 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-uni 3581  df-iun 3659 This theorem is referenced by:  dfiun2  3691  dfiun3g  4589  fniunfv  5401  iunexg  5746  uniqs  6164
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