Theorem elndif 2161

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 2160	. 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 957   \ cdif 2041

This theorem is referenced by:  peano5 3149  xrsupss 6035  xrinfmss 6036

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-12 967  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  ax-16 1209  ax-11o 1217  ax-ext 1458

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 980  df-sb 1171  df-clab 1463  df-cleq 1468  df-clel 1471  df-v 1809  df-dif 2046

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