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Theorem intsn 4266
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 4265 . 2  |-  ( A  e.  _V  ->  |^| { A }  =  A )
31, 2ax-mp 5 1  |-  |^| { A }  =  A
Colors of variables: wff setvar class
Syntax hints:    = wceq 1407    e. wcel 1844   _Vcvv 3061   {csn 3974   |^|cint 4229
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028  ax-ext 2382
This theorem depends on definitions:  df-bi 187  df-or 370  df-an 371  df-3an 978  df-tru 1410  df-ex 1636  df-nf 1640  df-sb 1766  df-clab 2390  df-cleq 2396  df-clel 2399  df-nfc 2554  df-ral 2761  df-v 3063  df-un 3421  df-in 3423  df-sn 3975  df-pr 3977  df-int 4230
This theorem is referenced by:  uniintsn  4267  intunsn  4269  op1stb  4663  op2ndb  5310  ssfii  7915  cf0  8665  cflecard  8667  uffix  20716  iotain  36185
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