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Theorem eldifn 3094
Description: Implication of membership in a class difference. (Contributed by NM, 3-May-1994.)
Assertion
Ref Expression
eldifn (𝐴 ∈ (𝐵𝐶) → ¬ 𝐴𝐶)

Proof of Theorem eldifn
StepHypRef Expression
1 eldif 2954 . 2 (𝐴 ∈ (𝐵𝐶) ↔ (𝐴𝐵 ∧ ¬ 𝐴𝐶))
21simprbi 264 1 (𝐴 ∈ (𝐵𝐶) → ¬ 𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wcel 1409  cdif 2941
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-dif 2947
This theorem is referenced by:  elndif  3095  unssin  3203  inssun  3204  noel  3255  disjel  3301  phpm  6357
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