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Theorem difss2 3419
Description: If a class is contained in a difference, it is contained in the minuend. (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
difss2  |-  ( A 
C_  ( B  \  C )  ->  A  C_  B )

Proof of Theorem difss2
StepHypRef Expression
1 id 20 . 2  |-  ( A 
C_  ( B  \  C )  ->  A  C_  ( B  \  C
) )
2 difss 3417 . 2  |-  ( B 
\  C )  C_  B
31, 2syl6ss 3303 1  |-  ( A 
C_  ( B  \  C )  ->  A  C_  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \ cdif 3260    C_ wss 3263
This theorem is referenced by:  difss2d  3420  sbthlem1  7153  bcthlem2  19147
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-v 2901  df-dif 3266  df-in 3270  df-ss 3277
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