Theorem elndif 3391

Description: A set does not belong to a class excluding it. (Contributed by NM, 27-Jun-1994.)

Assertion

Ref	Expression
elndif	⊢ (A ∈ B → ¬ A ∈ (C ∖ B))

Proof of Theorem elndif

Step	Hyp	Ref	Expression
1		eldifn 3390	. 2 ⊢ (A ∈ (C ∖ B) → ¬ A ∈ B)
2	1	con2i 112	1 ⊢ (A ∈ B → ¬ A ∈ (C ∖ B))

Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 1710   ∖ cdif 3207

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 2479  df-v 2862  df-nin 3212  df-compl 3213  df-in 3214  df-dif 3216

This theorem is referenced by: (None)