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Theorem difss2d 3702
 Description: If a class is contained in a difference, it is contained in the minuend. Deduction form of difss2 3701. (Contributed by David Moews, 1-May-2017.)
Hypothesis
Ref Expression
difss2d.1 (𝜑𝐴 ⊆ (𝐵𝐶))
Assertion
Ref Expression
difss2d (𝜑𝐴𝐵)

Proof of Theorem difss2d
StepHypRef Expression
1 difss2d.1 . 2 (𝜑𝐴 ⊆ (𝐵𝐶))
2 difss2 3701 . 2 (𝐴 ⊆ (𝐵𝐶) → 𝐴𝐵)
31, 2syl 17 1 (𝜑𝐴𝐵)
 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:  oacomf1olem  7531  numacn  8755  ramub1lem1  15568  ramub1lem2  15569  mreexexlem2d  16128  mreexexlem3d  16129  mreexexlem4d  16130  mreexexdOLD  16132  acsfiindd  17000  dpjidcl  18280  clsval2  20664  llycmpkgen2  21163  1stckgen  21167  alexsublem  21658  bcthlem3  22931  neibastop2lem  31525  eldioph2lem2  36342  limccog  38687  fourierdlem56  39055  fourierdlem95  39094
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