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Theorem neldifsnd 3738
Description:  A is not in  ( B  \  { A } ). Deduction form. (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
neldifsnd  |-  ( ph  ->  -.  A  e.  ( B  \  { A } ) )

Proof of Theorem neldifsnd
StepHypRef Expression
1 neldifsn 3737 . 2  |-  -.  A  e.  ( B  \  { A } )
21a1i 9 1  |-  ( ph  ->  -.  A  e.  ( B  \  { A } ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    e. wcel 2160    \ cdif 3141   {csn 3607
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ne 2361  df-v 2754  df-dif 3146  df-sn 3613
This theorem is referenced by:  difsnb  3750  frirrg  4365  elirr  4555
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