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Theorem elndif 3170
Description: A set does not belong to a class excluding it. (Contributed by NM, 27-Jun-1994.)
Assertion
Ref Expression
elndif  |-  ( A  e.  B  ->  -.  A  e.  ( C  \  B ) )

Proof of Theorem elndif
StepHypRef Expression
1 eldifn 3169 . 2  |-  ( A  e.  ( C  \  B )  ->  -.  A  e.  B )
21con2i 601 1  |-  ( A  e.  B  ->  -.  A  e.  ( C  \  B ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    e. wcel 1465    \ cdif 3038
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-dif 3043
This theorem is referenced by:  ddifnel  3177  inssdif  3282
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