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Theorem eldifn 3389
 Description: Implication of membership in a class difference. (Contributed by NM, 3-May-1994.)
Assertion
Ref Expression
eldifn (A (B C) → ¬ A C)

Proof of Theorem eldifn
StepHypRef Expression
1 eldif 3221 . 2 (A (B C) ↔ (A B ¬ A C))
21simprbi 450 1 (A (B C) → ¬ A C)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 1710   ∖ cdif 3206 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215 This theorem is referenced by:  elndif  3390  noel  3554  disjel  3597
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