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Theorem eldifn 3061
 Description: Implication of membership in a class difference. (Contributed by NM, 3-May-1994.)
Assertion
Ref Expression
eldifn (A (B𝐶) → ¬ A 𝐶)

Proof of Theorem eldifn
StepHypRef Expression
1 eldif 2921 . 2 (A (B𝐶) ↔ (A B ¬ A 𝐶))
21simprbi 260 1 (A (B𝐶) → ¬ A 𝐶)
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 1390   ∖ cdif 2908 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-dif 2914 This theorem is referenced by:  elndif  3062  unssin  3170  inssun  3171  noel  3222  disjel  3268
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