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Theorem sscond 3476
Description: If  A is contained in  B, then  ( C  \  B ) is contained in  ( C  \  A ). Deduction form of sscon 3473. (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 3473 . 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 3309    C_ wss 3312
This theorem is referenced by:  ssdif2d  3478  mapfien  7645  fin23lem26  8197  isercoll2  12454  fctop  17060  ntrss  17111  iunconlem  17482  clscon  17485  regr1lem  17763  blcld  18527  voliunlem1  19436
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-dif 3315  df-in 3319  df-ss 3326
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