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Theorem neldifsn 3897
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 2580 . 2  |-  -.  A  =/=  A
2 eldifsni 3896 . 2  |-  ( A  e.  ( B  \  { A } )  ->  A  =/=  A )
31, 2mto 169 1  |-  -.  A  e.  ( B  \  { A } )
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 1721    =/= wne 2575    \ cdif 3285   {csn 3782
This theorem is referenced by:  neldifsnd  3898  fofinf1o  7354  dfac9  7980  xrsupss  10851  islbs3  16190  ufinffr  17922  i1fd  19534  nbgranself2  21409  itg2addnclem  26163  itg2addnclem2  26164  prter2  26628  uvcff  27116  islindf4  27184
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 2393
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-ne 2577  df-v 2926  df-dif 3291  df-sn 3788
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