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Theorem dfiun2g 3999
 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 2664 . . . . . 6
2 rsp 2674 . . . . . . . 8
3 clel3g 2976 . . . . . . . 8
42, 3syl6 29 . . . . . . 7
54imp 418 . . . . . 6
61, 5rexbida 2629 . . . . 5
7 rexcom4 2878 . . . . 5
86, 7syl6bb 252 . . . 4
9 r19.41v 2764 . . . . . 6
109exbii 1582 . . . . 5
11 exancom 1586 . . . . 5
1210, 11bitri 240 . . . 4
138, 12syl6bb 252 . . 3
14 eliun 3973 . . 3
15 eluniab 3903 . . 3
1613, 14, 153bitr4g 279 . 2
1716eqrdv 2351 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wex 1541   wceq 1642   wcel 1710  cab 2339  wral 2614  wrex 2615  cuni 3891  ciun 3969 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-v 2861  df-uni 3892  df-iun 3971 This theorem is referenced by:  dfiun2  4001  uniqs  5984
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