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

Theorem neldifsn 3653
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 2317 . 2 ¬ 𝐴𝐴
2 eldifsni 3652 . 2 (𝐴 ∈ (𝐵 ∖ {𝐴}) → 𝐴𝐴)
31, 2mto 651 1 ¬ 𝐴 ∈ (𝐵 ∖ {𝐴})
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wcel 1480  wne 2308  cdif 3068  {csn 3527
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ne 2309  df-v 2688  df-dif 3073  df-sn 3533
This theorem is referenced by:  neldifsnd  3654  findcard2s  6784  fvsetsid  12003
  Copyright terms: Public domain W3C validator