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Theorem dfsn2 3574
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 3567 . 2 {𝐴, 𝐴} = ({𝐴} ∪ {𝐴})
2 unidm 3250 . 2 ({𝐴} ∪ {𝐴}) = {𝐴}
31, 2eqtr2i 2179 1 {𝐴} = {𝐴, 𝐴}
Colors of variables: wff set class
Syntax hints:   = wceq 1335  cun 3100  {csn 3560  {cpr 3561
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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106  df-pr 3567
This theorem is referenced by:  nfsn  3619  tpidm12  3658  tpidm  3661  preqsn  3738  opid  3759  unisn  3788  intsng  3841  opeqsn  4212  relop  4736  funopg  5204  enpr1g  6743  hashprg  10682  bj-snexg  13498
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