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Theorem conss1 43193
Description: Contrapositive law for subsets. (Contributed by Andrew Salmon, 15-Jul-2011.)
Assertion
Ref Expression
conss1 ((V ∖ 𝐴) ⊆ 𝐵 ↔ (V ∖ 𝐵) ⊆ 𝐴)

Proof of Theorem conss1
StepHypRef Expression
1 difcom 4488 1 ((V ∖ 𝐴) ⊆ 𝐵 ↔ (V ∖ 𝐵) ⊆ 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wb 205  Vcvv 3474  cdif 3945  wss 3948
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476  df-dif 3951  df-un 3953  df-in 3955  df-ss 3965
This theorem is referenced by: (None)
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