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Theorem iunid 3712
 Description: An indexed union of singletons recovers the index set. (Contributed by NM, 6-Sep-2005.)
Assertion
Ref Expression
iunid
Distinct variable group:   ,

Proof of Theorem iunid
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-sn 3381 . . . . 5
2 equcom 1593 . . . . . 6
32abbii 2153 . . . . 5
41, 3eqtri 2060 . . . 4
54a1i 9 . . 3
65iuneq2i 3675 . 2
7 iunab 3703 . . 3
8 risset 2352 . . . 4
98abbii 2153 . . 3
10 abid2 2158 . . 3
117, 9, 103eqtr2i 2066 . 2
126, 11eqtri 2060 1
 Colors of variables: wff set class Syntax hints:   wceq 1243   wcel 1393  cab 2026  wrex 2307  csn 3375  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-in 2924  df-ss 2931  df-sn 3381  df-iun 3659 This theorem is referenced by:  iunxpconst  4400  xpexgALT  5760  uniqs  6164
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