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Theorem difss2 3618
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 22 . 2  |-  ( A 
C_  ( B  \  C )  ->  A  C_  ( B  \  C
) )
2 difss 3616 . 2  |-  ( B 
\  C )  C_  B
31, 2syl6ss 3501 1  |-  ( A 
C_  ( B  \  C )  ->  A  C_  B )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \ cdif 3458    C_ wss 3461
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-v 3097  df-dif 3464  df-in 3468  df-ss 3475
This theorem is referenced by:  difss2d  3619  sbthlem1  7629  bcthlem2  21637  ismblfin  30030
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