Theorem conss1 43753

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

Step	Hyp	Ref	Expression
1		difcom 4481	1 ⊢ ((V ∖ 𝐴) ⊆ 𝐵 ↔ (V ∖ 𝐵) ⊆ 𝐴)

Syntax hints:   ↔ wb 205  Vcvv 3466   ∖ cdif 3938   ⊆ wss 3941

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958

This theorem is referenced by: (None)