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Theorem elndif 3273
Description: A set does not belong to a class excluding it. (Contributed by NM, 27-Jun-1994.)
Assertion
Ref Expression
elndif (𝐴𝐵 → ¬ 𝐴 ∈ (𝐶𝐵))

Proof of Theorem elndif
StepHypRef Expression
1 eldifn 3272 . 2 (𝐴 ∈ (𝐶𝐵) → ¬ 𝐴𝐵)
21con2i 628 1 (𝐴𝐵 → ¬ 𝐴 ∈ (𝐶𝐵))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wcel 2159  cdif 3140
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2170
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2175  df-cleq 2181  df-clel 2184  df-nfc 2320  df-v 2753  df-dif 3145
This theorem is referenced by:  ddifnel  3280  inssdif  3385
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