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Theorem dfsn2 3608
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 3601 . 2  |-  { A ,  A }  =  ( { A }  u.  { A } )
2 unidm 3280 . 2  |-  ( { A }  u.  { A } )  =  { A }
31, 2eqtr2i 2199 1  |-  { A }  =  { A ,  A }
Colors of variables: wff set class
Syntax hints:    = wceq 1353    u. cun 3129   {csn 3594   {cpr 3595
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2741  df-un 3135  df-pr 3601
This theorem is referenced by:  nfsn  3654  tpidm12  3693  tpidm  3696  preqsn  3777  opid  3798  unisn  3827  intsng  3880  opeqsn  4254  relop  4779  funopg  5252  enpr1g  6800  hashprg  10790  bj-snexg  14703
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