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Theorem difss2 4094
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 4092 . 2 (𝐵𝐶) ⊆ 𝐵
31, 2sstrdi 3957 1 (𝐴 ⊆ (𝐵𝐶) → 𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  cdif 3908  wss 3911
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3446  df-dif 3914  df-in 3918  df-ss 3928
This theorem is referenced by:  difss2d  4095  ssdifsn  4749  sbthlem1  9030  bcthlem2  24705  ismblfin  36165
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