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Theorem difss2d 3634
Description: If a class is contained in a difference, it is contained in the minuend. Deduction form of difss2 3633. (Contributed by David Moews, 1-May-2017.)
Hypothesis
Ref Expression
difss2d.1  |-  ( ph  ->  A  C_  ( B  \  C ) )
Assertion
Ref Expression
difss2d  |-  ( ph  ->  A  C_  B )

Proof of Theorem difss2d
StepHypRef Expression
1 difss2d.1 . 2  |-  ( ph  ->  A  C_  ( B  \  C ) )
2 difss2 3633 . 2  |-  ( A 
C_  ( B  \  C )  ->  A  C_  B )
31, 2syl 16 1  |-  ( ph  ->  A  C_  B )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \ cdif 3473    C_ wss 3476
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115  df-dif 3479  df-in 3483  df-ss 3490
This theorem is referenced by:  oacomf1olem  7213  numacn  8430  ramub1lem1  14403  ramub1lem2  14404  mreexexlem2d  14900  mreexexlem3d  14901  mreexexlem4d  14902  mreexexd  14903  acsfiindd  15664  dpjidcl  16909  dpjidclOLD  16916  clsval2  19345  llycmpkgen2  19814  1stckgen  19818  alexsublem  20307  bcthlem3  21528  neibastop2lem  29809  eldioph2lem2  30326  limccog  31190  fourierdlem56  31491  fourierdlem95  31530
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