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Theorem neldifsnd 3842
 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 3841 . 2 ¬ A (B {A})
21a1i 10 1 (φ → ¬ A (B {A}))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 1710   ∖ cdif 3206  {csn 3737 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-sn 3741 This theorem is referenced by:  difsnb  3850
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