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Theorem neldifsnd 3931
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 3930 . 2  |-  -.  A  e.  ( B  \  { A } )
21a1i 11 1  |-  ( ph  ->  -.  A  e.  ( B  \  { A } ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    e. wcel 1726    \ cdif 3318   {csn 3815
This theorem is referenced by:  difsnb  3941  fsnunf2  5933  rpnnen2lem9  12823  ramub1lem1  13395  ramub1lem2  13396  acsfiindd  14604  onint1  26200  prtlem80  26708
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-v 2959  df-dif 3324  df-sn 3821
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