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Theorem dfsn2 3597
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 3590 . 2 {𝐴, 𝐴} = ({𝐴} ∪ {𝐴})
2 unidm 3270 . 2 ({𝐴} ∪ {𝐴}) = {𝐴}
31, 2eqtr2i 2192 1 {𝐴} = {𝐴, 𝐴}
Colors of variables: wff set class
Syntax hints:   = wceq 1348  cun 3119  {csn 3583  {cpr 3584
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-un 3125  df-pr 3590
This theorem is referenced by:  nfsn  3643  tpidm12  3682  tpidm  3685  preqsn  3762  opid  3783  unisn  3812  intsng  3865  opeqsn  4237  relop  4761  funopg  5232  enpr1g  6776  hashprg  10743  bj-snexg  13947
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