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Theorem ssnel 4398
 Description: Relationship between subset and elementhood. In the context of ordinals this can be seen as an ordering law. (Contributed by Jim Kingdon, 22-Jul-2019.)
Assertion
Ref Expression
ssnel

Proof of Theorem ssnel
StepHypRef Expression
1 elirr 4370 . 2
2 ssel 3020 . 2
31, 2mtoi 626 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wcel 1439   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  ax-setind 4366 This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-ne 2257  df-ral 2365  df-v 2622  df-dif 3002  df-in 3006  df-ss 3013  df-sn 3456 This theorem is referenced by:  nntri1  6271
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