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Theorem unisn 3747
 Description: A set equals the union of its singleton. Theorem 8.2 of [Quine] p. 53. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
unisn.1
Assertion
Ref Expression
unisn

Proof of Theorem unisn
StepHypRef Expression
1 dfsn2 3536 . . 3
21unieqi 3741 . 2
3 unisn.1 . . 3
43, 3unipr 3745 . 2
5 unidm 3214 . 2
62, 4, 53eqtri 2162 1
 Colors of variables: wff set class Syntax hints:   wceq 1331   wcel 1480  cvv 2681   cun 3064  csn 3522  cpr 3523  cuni 3731 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-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420  df-v 2683  df-un 3070  df-sn 3528  df-pr 3529  df-uni 3732 This theorem is referenced by:  unisng  3748  uniintsnr  3802  unisuc  4330  op1sta  5015  op2nda  5018  elxp4  5021  uniabio  5093  iotass  5100  en1bg  6687
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