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Theorem difss2d 3773
Description: If a class is contained in a difference, it is contained in the minuend. Deduction form of difss2 3772. (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 3772 . 2 (𝐴 ⊆ (𝐵𝐶) → 𝐴𝐵)
31, 2syl 17 1 (𝜑𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  cdif 3604  wss 3607
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-v 3233  df-dif 3610  df-in 3614  df-ss 3621
This theorem is referenced by:  oacomf1olem  7689  numacn  8910  ramub1lem1  15777  ramub1lem2  15778  mreexexlem2d  16352  mreexexlem3d  16353  mreexexlem4d  16354  mreexexdOLD  16356  acsfiindd  17224  dpjidcl  18503  clsval2  20902  llycmpkgen2  21401  1stckgen  21405  alexsublem  21895  bcthlem3  23169  neibastop2lem  32480  eldioph2lem2  37641  limccog  40170  fourierdlem56  40697  fourierdlem95  40736
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