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Theorem intsn 3898
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 3897 . 2  |-  ( A  e.  _V  ->  |^| { A }  =  A )
31, 2ax-mp 8 1  |-  |^| { A }  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1623    e. wcel 1684   _Vcvv 2788   {csn 3640   |^|cint 3862
This theorem is referenced by:  uniintsn  3899  intunsn  3901  op1stb  4569  op2ndb  5156  ssfii  7172  cf0  7877  cflecard  7879  uffix  17616  iotain  27617
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-v 2790  df-un 3157  df-in 3159  df-sn 3646  df-pr 3647  df-int 3863
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