Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  oneluni Structured version   Unicode version

Theorem oneluni 4686
 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 4682 . 2
3 ssequn2 3512 . 2
42, 3sylib 189 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725   cun 3310   wss 3312  con0 4573 This theorem is referenced by:  onun2i  4689 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-v 2950  df-un 3317  df-in 3319  df-ss 3326  df-uni 4008  df-tr 4295  df-po 4495  df-so 4496  df-fr 4533  df-we 4535  df-ord 4576  df-on 4577
 Copyright terms: Public domain W3C validator