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Theorem sscond 3183
Description: If  A is contained in  B, then  ( C  \  B ) is contained in  ( C  \  A ). Deduction form of sscon 3180. (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 3180 . 2  |-  ( A 
C_  B  ->  ( C  \  B )  C_  ( C  \  A ) )
31, 2syl 14 1  |-  ( ph  ->  ( C  \  B
)  C_  ( C  \  A ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \ cdif 3038    C_ wss 3041
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-dif 3043  df-in 3047  df-ss 3054
This theorem is referenced by:  ssdif2d  3185  setsresg  11924
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