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Theorem ssdifd 3219
 Description: If 𝐴 is contained in 𝐵, then (𝐴 ∖ 𝐶) is contained in (𝐵 ∖ 𝐶). Deduction form of ssdif 3218. (Contributed by David Moews, 1-May-2017.)
Hypothesis
Ref Expression
ssdifd.1 (𝜑𝐴𝐵)
Assertion
Ref Expression
ssdifd (𝜑 → (𝐴𝐶) ⊆ (𝐵𝐶))

Proof of Theorem ssdifd
StepHypRef Expression
1 ssdifd.1 . 2 (𝜑𝐴𝐵)
2 ssdif 3218 . 2 (𝐴𝐵 → (𝐴𝐶) ⊆ (𝐵𝐶))
31, 2syl 14 1 (𝜑 → (𝐴𝐶) ⊆ (𝐵𝐶))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∖ cdif 3075   ⊆ wss 3078 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2123 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1732  df-clab 2128  df-cleq 2134  df-clel 2137  df-nfc 2272  df-v 2693  df-dif 3080  df-in 3084  df-ss 3091 This theorem is referenced by:  ssdif2d  3222  phplem4dom  6768  fisseneq  6837
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