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Theorem neldifsnd 3654
 Description: 𝐴 is not in (𝐵 ∖ {𝐴}). Deduction form. (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
neldifsnd (𝜑 → ¬ 𝐴 ∈ (𝐵 ∖ {𝐴}))

Proof of Theorem neldifsnd
StepHypRef Expression
1 neldifsn 3653 . 2 ¬ 𝐴 ∈ (𝐵 ∖ {𝐴})
21a1i 9 1 (𝜑 → ¬ 𝐴 ∈ (𝐵 ∖ {𝐴}))
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 1480   ∖ 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:  difsnb  3663  frirrg  4272  elirr  4456
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