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Theorem difssd 3116
Description: A difference of two classes is contained in the minuend. Deduction form of difss 3115. (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
difssd (𝜑 → (𝐴𝐵) ⊆ 𝐴)

Proof of Theorem difssd
StepHypRef Expression
1 difss 3115 . 2 (𝐴𝐵) ⊆ 𝐴
21a1i 9 1 (𝜑 → (𝐴𝐵) ⊆ 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4  cdif 2985  wss 2988
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2617  df-dif 2990  df-in 2994  df-ss 3001
This theorem is referenced by: (None)
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