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Theorem neldifsn 4149
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 2666 . 2  |-  -.  A  =/=  A
2 eldifsni 4148 . 2  |-  ( A  e.  ( B  \  { A } )  ->  A  =/=  A )
31, 2mto 176 1  |-  -.  A  e.  ( B  \  { A } )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    e. wcel 1762    =/= wne 2657    \ cdif 3468   {csn 4022
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1963  ax-ext 2440
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2448  df-cleq 2454  df-clel 2457  df-nfc 2612  df-ne 2659  df-v 3110  df-dif 3474  df-sn 4023
This theorem is referenced by:  neldifsnd  4150  fofinf1o  7792  dfac9  8507  xrsupss  11491  fvsetsid  14506  islbs3  17579  islindf4  18635  ufinffr  20160  i1fd  21818  nbgranself2  24100  itg2addnclem  29632  itg2addnclem2  29633  prter2  30215
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