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Theorem dfsn2 3455
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 3448 . 2  |-  { A ,  A }  =  ( { A }  u.  { A } )
2 unidm 3141 . 2  |-  ( { A }  u.  { A } )  =  { A }
31, 2eqtr2i 2109 1  |-  { A }  =  { A ,  A }
Colors of variables: wff set class
Syntax hints:    = wceq 1289    u. cun 2995   {csn 3441   {cpr 3442
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-un 3001  df-pr 3448
This theorem is referenced by:  nfsn  3497  tpidm12  3536  tpidm  3539  preqsn  3614  opid  3635  unisn  3664  intsng  3717  opeqsn  4070  relop  4574  funopg  5034  enpr1g  6495  hashprg  10181  bj-snexg  11460
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