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Theorem intsn 3872
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 3871 . 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 2763   {csn 3614   |^|cint 3836
This theorem is referenced by:  uniintsn  3873  intunsn  3875  op1stb  4541  op2ndb  5143  ssfii  7140  cf0  7845  cflecard  7847  uffix  17579  iotain  26986
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 2239
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 2245  df-cleq 2251  df-clel 2254  df-nfc 2383  df-ral 2523  df-v 2765  df-un 3132  df-in 3134  df-sn 3620  df-pr 3621  df-int 3837
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