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Theorem conss1 27750
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 3551 1  |-  ( ( _V  \  A ) 
C_  B  <->  ( _V  \  B )  C_  A
)
Colors of variables: wff set class
Syntax hints:    <-> wb 176   _Vcvv 2801    \ cdif 3162    C_ wss 3165
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179
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