Theorem elndif 1593

Description: A set does not belong to a class excluding it.

Assertion

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

Proof of Theorem elndif

Step	Hyp	Ref	Expression
1		eldifn 1592	. 2 ⊢ (A ∈ (C ∖ B) → ¬ A ∈ B)
2	1	con2i 89	1 ⊢ (A ∈ B → ¬ A ∈ (C ∖ B))

Syntax hints:  ¬ wn 1   → wi 2   ∈ wcel 1092   ∖ cdif 1484

This theorem is referenced by:  peano5 2394

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-dif 1489

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