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Theorem dfsn2 3541
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 3534 . 2  |-  { A ,  A }  =  ( { A }  u.  { A } )
2 unidm 3219 . 2  |-  ( { A }  u.  { A } )  =  { A }
31, 2eqtr2i 2161 1  |-  { A }  =  { A ,  A }
Colors of variables: wff set class
Syntax hints:    = wceq 1331    u. cun 3069   {csn 3527   {cpr 3528
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-pr 3534
This theorem is referenced by:  nfsn  3583  tpidm12  3622  tpidm  3625  preqsn  3702  opid  3723  unisn  3752  intsng  3805  opeqsn  4174  relop  4689  funopg  5157  enpr1g  6692  hashprg  10561  bj-snexg  13163
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