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Theorem sscond 3080
 Description: If 𝐴 is contained in 𝐵, then (𝐶 ∖ 𝐵) is contained in (𝐶 ∖ 𝐴). Deduction form of sscon 3077. (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 3077 . 2 (𝐴𝐵 → (𝐶𝐵) ⊆ (𝐶𝐴))
31, 2syl 14 1 (𝜑 → (𝐶𝐵) ⊆ (𝐶𝐴))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∖ cdif 2914   ⊆ wss 2917 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-dif 2920  df-in 2924  df-ss 2931 This theorem is referenced by:  ssdif2d  3082
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