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Theorem sscond 3313
Description: If  A is contained in  B, then  ( C  \  B ) is contained in  ( C  \  A ). Deduction form of sscon 3310. (Contributed by David Moews, 1-May-2017.)
Hypothesis
Ref Expression
ssdifd.1  |-  ( ph  ->  A  C_  B )
Assertion
Ref Expression
sscond  |-  ( ph  ->  ( C  \  B
)  C_  ( C  \  A ) )

Proof of Theorem sscond
StepHypRef Expression
1 ssdifd.1 . 2  |-  ( ph  ->  A  C_  B )
2 sscon 3310 . 2  |-  ( A 
C_  B  ->  ( C  \  B )  C_  ( C  \  A ) )
31, 2syl 15 1  |-  ( ph  ->  ( C  \  B
)  C_  ( C  \  A ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \ cdif 3149    C_ wss 3152
This theorem is referenced by:  ssdif2d  3315
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-dif 3155  df-in 3159  df-ss 3166
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