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Theorem difss2d 4109
 Description: If a class is contained in a difference, it is contained in the minuend. Deduction form of difss2 4108. (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 4108 . 2 (𝐴 ⊆ (𝐵𝐶) → 𝐴𝐵)
31, 2syl 17 1 (𝜑𝐴𝐵)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∖ cdif 3931   ⊆ wss 3934 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1905  ax-6 1964  ax-7 2009  ax-8 2110  ax-9 2118  ax-10 2139  ax-11 2154  ax-12 2170  ax-ext 2791 This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1534  df-ex 1775  df-nf 1779  df-sb 2064  df-clab 2798  df-cleq 2812  df-clel 2891  df-nfc 2961  df-v 3495  df-dif 3937  df-in 3941  df-ss 3950 This theorem is referenced by:  oacomf1olem  8182  numacn  9467  ramub1lem1  16354  ramub1lem2  16355  mreexexlem2d  16908  mreexexlem3d  16909  mreexexlem4d  16910  acsfiindd  17779  dpjidcl  19172  clsval2  21650  llycmpkgen2  22150  1stckgen  22154  alexsublem  22644  bcthlem3  23921  pmtrcnelor  30728  lfuhgr  32357  neibastop2lem  33701  pibt2  34690  eldioph2lem2  39348  limccog  41890  fourierdlem56  42437  fourierdlem95  42476
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