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Theorem neldifsn 3527
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 2255 . 2  |-  -.  A  =/=  A
2 eldifsni 3526 . 2  |-  ( A  e.  ( B  \  { A } )  ->  A  =/=  A )
31, 2mto 621 1  |-  -.  A  e.  ( B  \  { A } )
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 1434    =/= wne 2246    \ cdif 2971   {csn 3406
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ne 2247  df-v 2604  df-dif 2976  df-sn 3412
This theorem is referenced by:  neldifsnd  3528  findcard2s  6424
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