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Theorem onelini 4696
 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 4693 . 2
3 dfss 3337 . 2
42, 3sylib 190 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653   wcel 1726   cin 3321   wss 3322  con0 4584 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-v 2960  df-in 3329  df-ss 3336  df-uni 4018  df-tr 4306  df-po 4506  df-so 4507  df-fr 4544  df-we 4546  df-ord 4587  df-on 4588
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