Theorem eldifi 2152

Description: Implication of membership in a class difference.

Assertion

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

Proof of Theorem eldifi

Step	Hyp	Ref	Expression
1		eldif 2047	. 2 |- (A e. (B \ C) <-> (A e. B /\ -. A e. C))
2	1	pm3.26bi 322	1 |- (A e. (B \ C) -> A e. B)

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

This theorem is referenced by:  difss 2157  tz7.7 2963  tfi 3116  peano5 3143  tz7.48-1 3941  tz7.49 3944  pssnn 4513  unblem1 4517  pwfilem 4544  inf3lem3 4587  acdc3lem 7428  acdc2lem1 7430  acdclem 7436  bcthlem33 7965  ablmul 8068  mulid 8069  effoi 8666  effoiOLD 8667  strlem1 10087  strlem3 10090  strlem4 10091  strlem5 10092  hstrlem3 10098  hstrlem4 10099

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

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