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Theorem inssddif 3241
 Description: Intersection of two classes and class difference. In classical logic, such as Exercise 4.10(q) of [Mendelson] p. 231, this is an equality rather than subset. (Contributed by Jim Kingdon, 26-Jul-2018.)
Assertion
Ref Expression
inssddif

Proof of Theorem inssddif
StepHypRef Expression
1 inss1 3221 . . 3
2 ssddif 3234 . . 3
31, 2mpbi 144 . 2
4 difin 3237 . . 3
54difeq2i 3116 . 2
63, 5sseqtri 3059 1
 Colors of variables: wff set class Syntax hints:   cdif 2997   cin 2999   wss 3000 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 580  ax-in2 581  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-tru 1293  df-fal 1296  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-ral 2365  df-rab 2369  df-v 2622  df-dif 3002  df-in 3006  df-ss 3013 This theorem is referenced by: (None)
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