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Theorem dfsn2 3417
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 3410 . 2  |-  { A ,  A }  =  ( { A }  u.  { A } )
2 unidm 3114 . 2  |-  ( { A }  u.  { A } )  =  { A }
31, 2eqtr2i 2077 1  |-  { A }  =  { A ,  A }
Colors of variables: wff set class
Syntax hints:    = wceq 1259    u. cun 2943   {csn 3403   {cpr 3404
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-pr 3410
This theorem is referenced by:  nfsn  3458  tpidm12  3497  tpidm  3500  preqsn  3574  opid  3595  unisn  3624  intsng  3677  opeqsn  4017  relop  4514  funopg  4962  enpr1g  6309  bj-snexg  10419
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