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Theorem sscond 3074
 Description: If A is contained in B, then (𝐶 ∖ B) is contained in (𝐶 ∖ A). Deduction form of sscon 3071. (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 3071 . 2 (AB → (𝐶B) ⊆ (𝐶A))
31, 2syl 14 1 (φ → (𝐶B) ⊆ (𝐶A))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∖ cdif 2908   ⊆ wss 2911 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-dif 2914  df-in 2918  df-ss 2925 This theorem is referenced by:  ssdif2d  3076
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