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Theorem neldifsn 3827
Description:  A is not in  ( B  \  { A } ). (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
neldifsn  |-  -.  A  e.  ( B  \  { A } )

Proof of Theorem neldifsn
StepHypRef Expression
1 neirr 2526 . 2  |-  -.  A  =/=  A
2 eldifsni 3826 . 2  |-  ( A  e.  ( B  \  { A } )  ->  A  =/=  A )
31, 2mto 167 1  |-  -.  A  e.  ( B  \  { A } )
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 1710    =/= wne 2521    \ cdif 3225   {csn 3716
This theorem is referenced by:  neldifsnd  3828  itg2addnclem  25492  itg2addnclem2  25493  nbgranself2  27602
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ne 2523  df-v 2866  df-dif 3231  df-sn 3722
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