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Theorem dfsn2 3621
Description: Alternate definition of singleton. Definition 5.1 of [TakeutiZaring] p. 15. (Contributed by NM, 24-Apr-1994.)
Assertion
Ref Expression
dfsn2 {𝐴} = {𝐴, 𝐴}

Proof of Theorem dfsn2
StepHypRef Expression
1 df-pr 3614 . 2 {𝐴, 𝐴} = ({𝐴} ∪ {𝐴})
2 unidm 3293 . 2 ({𝐴} ∪ {𝐴}) = {𝐴}
31, 2eqtr2i 2211 1 {𝐴} = {𝐴, 𝐴}
Colors of variables: wff set class
Syntax hints:   = wceq 1364  cun 3142  {csn 3607  {cpr 3608
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-pr 3614
This theorem is referenced by:  nfsn  3667  tpidm12  3706  tpidm  3709  preqsn  3790  opid  3811  unisn  3840  intsng  3893  opeqsn  4270  relop  4795  funopg  5269  enpr1g  6824  hashprg  10820  bj-snexg  15122
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