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Theorem difss2d 3422
Description: If a class is contained in a difference, it is contained in the minuend. Deduction form of difss2 3421. (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 3421 . 2  |-  ( A 
C_  ( B  \  C )  ->  A  C_  B )
31, 2syl 16 1  |-  ( ph  ->  A  C_  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \ cdif 3262    C_ wss 3265
This theorem is referenced by:  oacomf1olem  6745  numacn  7865  ramub1lem1  13323  ramub1lem2  13324  mreexexlem2d  13799  mreexexlem3d  13800  mreexexlem4d  13801  mreexexd  13802  acsfiindd  14532  dpjidcl  15545  clsval2  17039  llycmpkgen2  17505  1stckgen  17509  alexsublem  17998  bcthlem3  19150  neibastop2lem  26082  eldioph2lem2  26512
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 2370
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 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-v 2903  df-dif 3268  df-in 3272  df-ss 3279
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