Theorem dfsn2 1819

Description: Alternate definition of singleton. Definition 5.1 of [TakeutiZaring] p. 15.

Assertion

Ref	Expression
dfsn2	|- {A} = {A, A}

Proof of Theorem dfsn2

Step	Hyp	Ref	Expression
1		df-pr 1812	. 2 |- {A, A} = ({A} u. {A})
2		unidm 1603	. 2 |- ({A} u. {A}) = {A}
3	1, 2	eqtr2 1120	1 |- {A} = {A, A}

Syntax hints:   = wceq 1091   u. cun 1485  {csn 1808  {cpr 1809

This theorem is referenced by:  elsncg 1825  hbsn 1833  opprc2 1907  opprc3 1908  unisn 1932  intsn 1991  dmsnsnsn 2548

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-un 1490  df-pr 1812

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