Theorem eldifn 2215

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 2109	. 2 |- (A e. (B \ C) <-> (A e. B /\ -. A e. C))
2	1	pm3.27bi 324	1 |- (A e. (B \ C) -> -. A e. C)

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

This theorem is referenced by:  elndif 2216  tz7.7 3001  tfi 3207  peano5 3241  tz7.48-2 4258  tz7.49 4260  inf3lem3 4760  setind 4794  acdc3lem 7697  acdc2lem1 7700  acdclem 7706  clsval2 7895  elcls 7914  bcthlem28 8237  strlem1 10458  hscptsscld 11491  ist1-2 11603  ufprim 11654  difxp 11798  recms 12066

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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