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Theorem sscond 3137
Description: If 𝐴 is contained in 𝐵, then (𝐶𝐵) is contained in (𝐶𝐴). Deduction form of sscon 3134. (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 3134 . 2 (𝐴𝐵 → (𝐶𝐵) ⊆ (𝐶𝐴))
31, 2syl 14 1 (𝜑 → (𝐶𝐵) ⊆ (𝐶𝐴))
Colors of variables: wff set class
Syntax hints:  wi 4  cdif 2996  wss 2999
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-dif 3001  df-in 3005  df-ss 3012
This theorem is referenced by:  ssdif2d  3139  setsresg  11532
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