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Theorem intsn 4046
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 4045 . 2  |-  ( A  e.  _V  ->  |^| { A }  =  A )
31, 2ax-mp 8 1  |-  |^| { A }  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1649    e. wcel 1721   _Vcvv 2916   {csn 3774   |^|cint 4010
This theorem is referenced by:  uniintsn  4047  intunsn  4049  op1stb  4717  op2ndb  5312  ssfii  7382  cf0  8087  cflecard  8089  uffix  17906  iotain  27485
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ral 2671  df-v 2918  df-un 3285  df-in 3287  df-sn 3780  df-pr 3781  df-int 4011
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