ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  neldifsn Unicode version

Theorem neldifsn 3497
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 2215 . 2  |-  -.  A  =/=  A
2 eldifsni 3496 . 2  |-  ( A  e.  ( B  \  { A } )  ->  A  =/=  A )
31, 2mto 588 1  |-  -.  A  e.  ( B  \  { A } )
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 1393    =/= wne 2204    \ cdif 2914   {csn 3375
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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ne 2206  df-v 2559  df-dif 2920  df-sn 3381
This theorem is referenced by:  neldifsnd  3498  findcard2s  6347
  Copyright terms: Public domain W3C validator