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Theorem sscond 3428
Description: If  A is contained in  B, then  ( C  \  B ) is contained in  ( C  \  A ). Deduction form of sscon 3425. (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 3425 . 2  |-  ( A 
C_  B  ->  ( C  \  B )  C_  ( C  \  A ) )
31, 2syl 16 1  |-  ( ph  ->  ( C  \  B
)  C_  ( C  \  A ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \ cdif 3261    C_ wss 3264
This theorem is referenced by:  ssdif2d  3430  mapfien  7587  fin23lem26  8139  isercoll2  12390  fctop  16992  ntrss  17043  iunconlem  17412  clscon  17415  regr1lem  17693  blcld  18426  voliunlem1  19312
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 2369
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 2375  df-cleq 2381  df-clel 2384  df-nfc 2513  df-v 2902  df-dif 3267  df-in 3271  df-ss 3278
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