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Theorem dfsn2 3747
 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 3742 . 2 {A, A} = ({A} ∪ {A})
2 unidm 3407 . 2 ({A} ∪ {A}) = {A}
31, 2eqtr2i 2374 1 {A} = {A, A}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ∪ cun 3207  {csn 3737  {cpr 3738 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-pr 3742 This theorem is referenced by:  nfsn  3784  tpidm12  3821  tpidm  3824  unisn  3907  intsng  3961
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