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Theorem dfiun3g 4791
 Description: Alternate definition of indexed union when is a set. (Contributed by Mario Carneiro, 31-Aug-2015.)
Assertion
Ref Expression
dfiun3g

Proof of Theorem dfiun3g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfiun2g 3840 . 2
2 eqid 2137 . . . 4
32rnmpt 4782 . . 3
43unieqi 3741 . 2
51, 4syl6eqr 2188 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1331   wcel 1480  cab 2123  wral 2414  wrex 2415  cuni 3731  ciun 3808   cmpt 3984   crn 4535 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119  ax-sep 4041  ax-pow 4093  ax-pr 4126 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2000  df-mo 2001  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419  df-rex 2420  df-v 2683  df-un 3070  df-in 3072  df-ss 3079  df-pw 3507  df-sn 3528  df-pr 3529  df-op 3531  df-uni 3732  df-iun 3810  df-br 3925  df-opab 3985  df-mpt 3986  df-cnv 4542  df-dm 4544  df-rn 4545 This theorem is referenced by:  dfiun3  4793  iunon  6174  tgiun  12231
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