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Theorem intsn 3839
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 3838 . 2  |-  ( A  e.  _V  ->  |^| { A }  =  A )
31, 2ax-mp 10 1  |-  |^| { A }  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1619    e. wcel 1621   _Vcvv 2740   {csn 3581   |^|cint 3803
This theorem is referenced by:  uniintsn  3840  intunsn  3842  op1stb  4506  op2ndb  5108  ssfii  7105  cf0  7810  cflecard  7812  uffix  17543  iotain  26950
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-ral 2520  df-v 2742  df-un 3099  df-in 3101  df-sn 3587  df-pr 3588  df-int 3804
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