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Theorem neldifsn 4101
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 2609 . 2  |-  -.  A  =/=  A
2 eldifsni 4100 . 2  |-  ( A  e.  ( B  \  { A } )  ->  A  =/=  A )
31, 2mto 178 1  |-  -.  A  e.  ( B  \  { A } )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    e. wcel 1844    =/= wne 2600    \ cdif 3413   {csn 3974
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028  ax-ext 2382
This theorem depends on definitions:  df-bi 187  df-an 371  df-tru 1410  df-ex 1636  df-nf 1640  df-sb 1766  df-clab 2390  df-cleq 2396  df-clel 2399  df-nfc 2554  df-ne 2602  df-v 3063  df-dif 3419  df-sn 3975
This theorem is referenced by:  neldifsnd  4102  fofinf1o  7837  dfac9  8550  xrsupss  11555  fvsetsid  14870  islbs3  18123  islindf4  19167  ufinffr  20724  i1fd  22382  nbgranself2  24865  itg2addnclem  31452  itg2addnclem2  31453  prter2  31917
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