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Theorem ssindif0im 3348
 Description: Subclass implies empty intersection with difference from the universal class. (Contributed by NM, 17-Sep-2003.)
Assertion
Ref Expression
ssindif0im

Proof of Theorem ssindif0im
StepHypRef Expression
1 ddifss 3240 . . 3
2 sstr 3036 . . 3
31, 2mpan2 417 . 2
4 disj2 3344 . 2
53, 4sylibr 133 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1290  cvv 2622   cdif 2999   cin 3001   wss 3002  c0 3289 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-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-ral 2365  df-v 2624  df-dif 3004  df-in 3008  df-ss 3015  df-nul 3290 This theorem is referenced by: (None)
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