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Theorem difss2 4107
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 4105 . 2 (𝐵𝐶) ⊆ 𝐵
31, 2sstrdi 3976 1 (𝐴 ⊆ (𝐵𝐶) → 𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  cdif 3930  wss 3933
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-v 3494  df-dif 3936  df-in 3940  df-ss 3949
This theorem is referenced by:  difss2d  4108  ssdifsn  4712  sbthlem1  8615  bcthlem2  23855  ismblfin  34814
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