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Theorem oneluni 4948
Description: An ordinal number equals its union with any element. (Contributed by NM, 13-Jun-1994.)
Hypothesis
Ref Expression
on.1
Assertion
Ref Expression
oneluni

Proof of Theorem oneluni
StepHypRef Expression
1 on.1 . . 3
21onelssi 4944 . 2
3 ssequn2 3643 . 2
42, 3sylib 196 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1370  e.wcel 1758  u.cun 3440  C_wss 3442   con0 4836
This theorem is referenced by:  onun2i  4951
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ral 2805  df-rex 2806  df-v 3083  df-un 3447  df-in 3449  df-ss 3456  df-uni 4209  df-tr 4503  df-po 4758  df-so 4759  df-fr 4796  df-we 4798  df-ord 4839  df-on 4840
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