Theorem elndif 2216

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

Assertion

Ref	Expression
elndif	|- (A e. B -> -. A e. (C \ B))

Proof of Theorem elndif

Step	Hyp	Ref	Expression
1		eldifn 2215	. 2 |- (A e. (C \ B) -> -. A e. B)
2	1	con2i 97	1 |- (A e. B -> -. A e. (C \ B))

Syntax hints:  -. wn 2   -> wi 3   e. wcel 994   \ cdif 2096

This theorem is referenced by:  peano5 3241  xrsupss 6246  xrinfmss 6247  subntr 11482  cptclsscpt 11489  ist1-2 11603  ufinffr 11663  dif1en 11833

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 998  ax-gen 999  ax-8 1000  ax-10 1002  ax-12 1004  ax-17 1007  ax-4 1009  ax-5o 1011  ax-6o 1014  ax-9o 1159  ax-10o 1177  ax-16 1247  ax-11o 1255  ax-ext 1500

This theorem depends on definitions:  df-bi 145  df-an 223  df-ex 1017  df-sb 1209  df-clab 1506  df-cleq 1511  df-clel 1514  df-v 1858  df-dif 2101

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