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Theorem sscond 4142
Description: If 𝐴 is contained in 𝐵, then (𝐶𝐵) is contained in (𝐶𝐴). Deduction form of sscon 4139. (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 4139 . 2 (𝐴𝐵 → (𝐶𝐵) ⊆ (𝐶𝐴))
31, 2syl 17 1 (𝜑 → (𝐶𝐵) ⊆ (𝐶𝐴))
Colors of variables: wff setvar class
Syntax hints:  wi 4  cdif 3946  wss 3949
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-dif 3952  df-in 3956  df-ss 3966
This theorem is referenced by:  ssdif2d  4144  eldifeldifsn  4815  fin23lem26  10320  isercoll2  15615  fctop  22507  ntrss  22559  iunconnlem  22931  clsconn  22934  regr1lem  23243  blcld  24014  rrxdstprj1  24926  voliunlem1  25067  elrspunidl  32546  carsgclctunlem2  33318  salexct  45050  meaiininclem  45202  carageniuncllem2  45238  seposep  47558
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