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Theorem dfsn2 3420
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 3413 . 2 {𝐴, 𝐴} = ({𝐴} ∪ {𝐴})
2 unidm 3116 . 2 ({𝐴} ∪ {𝐴}) = {𝐴}
31, 2eqtr2i 2103 1 {𝐴} = {𝐴, 𝐴}
Colors of variables: wff set class
Syntax hints:   = wceq 1285  cun 2972  {csn 3406  {cpr 3407
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-pr 3413
This theorem is referenced by:  nfsn  3460  tpidm12  3499  tpidm  3502  preqsn  3575  opid  3596  unisn  3625  intsng  3678  opeqsn  4015  relop  4514  funopg  4964  enpr1g  6345  sizeprg  9832  bj-snexg  10861
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