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Theorem conss1 27316
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 3656 1  |-  ( ( _V  \  A ) 
C_  B  <->  ( _V  \  B )  C_  A
)
Colors of variables: wff set class
Syntax hints:    <-> wb 177   _Vcvv 2900    \ cdif 3261    C_ wss 3264
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-un 3269  df-in 3271  df-ss 3278
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