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Theorem conss1 27614
Description: Contrapositive law for subsets. (Contributed by Andrew Salmon, 15-Jul-2011.)
Assertion
Ref Expression
conss1  |-  ( ( _V  \  A ) 
C_  B  <->  ( _V  \  B )  C_  A
)

Proof of Theorem conss1
StepHypRef Expression
1 difcom 3704 1  |-  ( ( _V  \  A ) 
C_  B  <->  ( _V  \  B )  C_  A
)
Colors of variables: wff set class
Syntax hints:    <-> wb 177   _Vcvv 2948    \ cdif 3309    C_ wss 3312
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-un 3317  df-in 3319  df-ss 3326
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