Theorem elndif 2154

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 2153	. 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 955   \ cdif 2034

This theorem is referenced by:  peano5 3143  xrsupss 6025  xrinfmss 6026

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-v 1803  df-dif 2039

Copyright terms: Public domain