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Theorem neldifsn 3488
Description: A is not in (B ∖ {A}). (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
neldifsn ¬ A (B ∖ {A})

Proof of Theorem neldifsn
StepHypRef Expression
1 neirr 2210 . 2 ¬ AA
2 eldifsni 3487 . 2 (A (B ∖ {A}) → AA)
31, 2mto 587 1 ¬ A (B ∖ {A})
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   wcel 1390  wne 2201  cdif 2908  {csn 3367
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ne 2203  df-v 2553  df-dif 2914  df-sn 3373
This theorem is referenced by:  neldifsnd  3489
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