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Theorem dfsn2 3386
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 3379 . 2  |-  { A ,  A }  =  ( { A }  u.  { A } )
2 unidm 3083 . 2  |-  ( { A }  u.  { A } )  =  { A }
31, 2eqtr2i 2061 1  |-  { A }  =  { A ,  A }
Colors of variables: wff set class
Syntax hints:    = wceq 1243    u. cun 2912   {csn 3372   {cpr 3373
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2556  df-un 2919  df-pr 3379
This theorem is referenced by:  nfsn  3427  tpidm12  3466  tpidm  3469  preqsn  3543  opid  3564  unisn  3593  intsng  3646  opeqsn  3986  relop  4473  funopg  4921  enpr1g  6265  bj-snexg  9905
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