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Theorem dmsnsnsng 5011
 Description: The domain of the singleton of the singleton of a singleton. (Contributed by Jim Kingdon, 16-Dec-2018.)
Assertion
Ref Expression
dmsnsnsng

Proof of Theorem dmsnsnsng
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2684 . . . . . . 7
21opid 3718 . . . . . 6
3 sneq 3533 . . . . . . 7
43sneqd 3535 . . . . . 6
52, 4syl5eq 2182 . . . . 5
65sneqd 3535 . . . 4
76dmeqd 4736 . . 3
87, 3eqeq12d 2152 . 2
91dmsnop 5007 . 2
108, 9vtoclg 2741 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1331   wcel 1480  cvv 2681  csn 3522  cop 3525   cdm 4534 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-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  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-br 3925  df-dm 4544 This theorem is referenced by: (None)
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