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Theorem difss2 3468
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 3466 . 2  |-  ( B 
\  C )  C_  B
31, 2syl6ss 3352 1  |-  ( A 
C_  ( B  \  C )  ->  A  C_  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \ cdif 3309    C_ wss 3312
This theorem is referenced by:  difss2d  3469  sbthlem1  7209  bcthlem2  19270  ismblfin  26237
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-dif 3315  df-in 3319  df-ss 3326
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