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Theorem neldifsnd 4143
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 4142 . 2  |-  -.  A  e.  ( B  \  { A } )
21a1i 11 1  |-  ( ph  ->  -.  A  e.  ( B  \  { A } ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    e. wcel 1804    \ cdif 3458   {csn 4014
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ne 2640  df-v 3097  df-dif 3464  df-sn 4015
This theorem is referenced by:  difsnb  4157  fsnunf2  6095  rpnnen2lem9  13833  ramub1lem1  14421  ramub1lem2  14422  acsfiindd  15681  gsummgp0  17130  islindf4  18746  gsummatr01lem3  19032  onint1  29889  prtlem80  30574  fsumsplitsndif  32184  mgpsumunsn  32684
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