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Theorem ssdifssd 3327
Description: If  A is contained in  B, then  ( A  \  C ) is also contained in  B. Deduction form of ssdifss 3320. (Contributed by David Moews, 1-May-2017.)
Hypothesis
Ref Expression
ssdifd.1  |-  ( ph  ->  A  C_  B )
Assertion
Ref Expression
ssdifssd  |-  ( ph  ->  ( A  \  C
)  C_  B )

Proof of Theorem ssdifssd
StepHypRef Expression
1 ssdifd.1 . 2  |-  ( ph  ->  A  C_  B )
2 ssdifss 3320 . 2  |-  ( A 
C_  B  ->  ( A  \  C )  C_  B )
31, 2syl 15 1  |-  ( ph  ->  ( A  \  C
)  C_  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \ cdif 3162    C_ wss 3165
This theorem is referenced by:  mrieqvlemd  13547  mrieqv2d  13557  mrissmrid  13559  mreexmrid  13561  mreexexlem2d  13563  mreexexlem4d  13565  acsfiindd  14296  ftc1cnnc  25025
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-dif 3168  df-in 3172  df-ss 3179
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