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Theorem intsn 3914
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 3913 . 2  |-  ( A  e.  _V  ->  |^| { A }  =  A )
31, 2ax-mp 8 1  |-  |^| { A }  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1632    e. wcel 1696   _Vcvv 2801   {csn 3653   |^|cint 3878
This theorem is referenced by:  uniintsn  3915  intunsn  3917  op1stb  4585  op2ndb  5172  ssfii  7188  cf0  7893  cflecard  7895  uffix  17632  iotain  27720
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-v 2803  df-un 3170  df-in 3172  df-sn 3659  df-pr 3660  df-int 3879
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