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Theorem difss2d 3938
Description: If a class is contained in a difference, it is contained in the minuend. Deduction form of difss2 3937. (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 3937 . 2 (𝐴 ⊆ (𝐵𝐶) → 𝐴𝐵)
31, 2syl 17 1 (𝜑𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  cdif 3766  wss 3769
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-ext 2777
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2786  df-cleq 2792  df-clel 2795  df-nfc 2930  df-v 3387  df-dif 3772  df-in 3776  df-ss 3783
This theorem is referenced by:  oacomf1olem  7884  numacn  9158  ramub1lem1  16063  ramub1lem2  16064  mreexexlem2d  16620  mreexexlem3d  16621  mreexexlem4d  16622  acsfiindd  17492  dpjidcl  18773  clsval2  21183  llycmpkgen2  21682  1stckgen  21686  alexsublem  22176  bcthlem3  23452  neibastop2lem  32867  eldioph2lem2  38110  limccog  40596  fourierdlem56  41122  fourierdlem95  41161
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