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Theorem intsn 3900
Description: The intersection of a singleton is its member. Theorem 70 of [Suppes] p. 41. (Contributed by NM, 29-Sep-2002.)
Hypothesis
Ref Expression
intsn.1  |-  A  e. 
_V
Assertion
Ref Expression
intsn  |-  |^| { A }  =  A

Proof of Theorem intsn
StepHypRef Expression
1 intsn.1 . 2  |-  A  e. 
_V
2 intsng 3899 . 2  |-  ( A  e.  _V  ->  |^| { A }  =  A )
31, 2ax-mp 8 1  |-  |^| { A }  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1625    e. wcel 1686   _Vcvv 2790   {csn 3642   |^|cint 3864
This theorem is referenced by:  uniintsn  3901  intunsn  3903  op1stb  4571  op2ndb  5158  ssfii  7174  cf0  7879  cflecard  7881  uffix  17618  iotain  27628
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-7 1710  ax-11 1717  ax-12 1868  ax-ext 2266
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1531  df-nf 1534  df-sb 1632  df-clab 2272  df-cleq 2278  df-clel 2281  df-nfc 2410  df-ral 2550  df-v 2792  df-un 3159  df-in 3161  df-sn 3648  df-pr 3649  df-int 3865
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