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Theorem onelini 4167
 Description: An element of an ordinal number equals the intersection with it. (Contributed by NM, 11-Jun-1994.)
Hypothesis
Ref Expression
on.1
Assertion
Ref Expression
onelini

Proof of Theorem onelini
StepHypRef Expression
1 on.1 . . 3
21onelssi 4166 . 2
3 dfss 2932 . 2
42, 3sylib 127 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243   wcel 1393   cin 2916   wss 2917  con0 4100 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-in 2924  df-ss 2931  df-uni 3581  df-tr 3855  df-iord 4103  df-on 4105 This theorem is referenced by: (None)
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