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Theorem difss2d 4095
Description: If a class is contained in a difference, it is contained in the minuend. Deduction form of difss2 4094. (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 4094 . 2 (𝐴 ⊆ (𝐵𝐶) → 𝐴𝐵)
31, 2syl 17 1 (𝜑𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  cdif 3908  wss 3911
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3446  df-dif 3914  df-in 3918  df-ss 3928
This theorem is referenced by:  oacomf1olem  8512  numacn  9990  ramub1lem1  16903  ramub1lem2  16904  mreexexlem2d  17530  mreexexlem3d  17531  mreexexlem4d  17532  acsfiindd  18447  dpjidcl  19842  clsval2  22417  llycmpkgen2  22917  1stckgen  22921  alexsublem  23411  bcthlem3  24706  pmtrcnelor  31991  lfuhgr  33768  neibastop2lem  34878  pibt2  35934  eldioph2lem2  41127  limccog  43947  fourierdlem56  44489  fourierdlem95  44528
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