Theorem eldifn 2153

Description: Implication of membership in a class difference.

Assertion

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

Proof of Theorem eldifn

Step	Hyp	Ref	Expression
1		eldif 2047	. 2 |- (A e. (B \ C) <-> (A e. B /\ -. A e. C))
2	1	pm3.27bi 326	1 |- (A e. (B \ C) -> -. A e. C)

Syntax hints:  -. wn 2   -> wi 3   e. wcel 955   \ cdif 2034

This theorem is referenced by:  elndif 2154  tz7.7 2963  tfi 3116  peano5 3143  tz7.48-2 3942  tz7.49 3944  inf3lem3 4587  setind 4620  acdc3lem 7428  acdc2lem1 7430  acdclem 7436  clsval2 7627  elcls 7646  bcthlem28 7960  effoiOLD 8667  strlem1 10087

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