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Theorem sscond 3709
 Description: If 𝐴 is contained in 𝐵, then (𝐶 ∖ 𝐵) is contained in (𝐶 ∖ 𝐴). Deduction form of sscon 3706. (Contributed by David Moews, 1-May-2017.)
Hypothesis
Ref Expression
ssdifd.1 (𝜑𝐴𝐵)
Assertion
Ref Expression
sscond (𝜑 → (𝐶𝐵) ⊆ (𝐶𝐴))

Proof of Theorem sscond
StepHypRef Expression
1 ssdifd.1 . 2 (𝜑𝐴𝐵)
2 sscon 3706 . 2 (𝐴𝐵 → (𝐶𝐵) ⊆ (𝐶𝐴))
31, 2syl 17 1 (𝜑 → (𝐶𝐵) ⊆ (𝐶𝐴))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∖ cdif 3537   ⊆ wss 3540 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-dif 3543  df-in 3547  df-ss 3554 This theorem is referenced by:  ssdif2d  3711  fin23lem26  9030  isercoll2  14247  fctop  20618  ntrss  20669  iunconlem  21040  clscon  21043  regr1lem  21352  blcld  22120  rrxdstprj1  23000  voliunlem1  23125  carsgclctunlem2  29708  salexct  39228  meaiininclem  39376  carageniuncllem2  39412
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