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Theorem difss2 3701
Description: If a class is contained in a difference, it is contained in the minuend. (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
difss2 (𝐴 ⊆ (𝐵𝐶) → 𝐴𝐵)

Proof of Theorem difss2
StepHypRef Expression
1 id 22 . 2 (𝐴 ⊆ (𝐵𝐶) → 𝐴 ⊆ (𝐵𝐶))
2 difss 3699 . 2 (𝐵𝐶) ⊆ 𝐵
31, 2syl6ss 3580 1 (𝐴 ⊆ (𝐵𝐶) → 𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  cdif 3537  wss 3540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-dif 3543  df-in 3547  df-ss 3554
This theorem is referenced by:  difss2d  3702  sbthlem1  7955  bcthlem2  22930  ismblfin  32620
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