Theorem oneluni 4995

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

Step	Hyp	Ref	Expression
1		on.1	. . 3
2	1	onelssi 4991	. 2
3		ssequn2 3676	. 2
4	2, 3	sylib 196	1

Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  u.cun 3473  C_wss 3475  con0 4883

This theorem is referenced by:  onun2i  4998

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111  df-un 3480  df-in 3482  df-ss 3489  df-uni 4250  df-tr 4546  df-po 4805  df-so 4806  df-fr 4843  df-we 4845  df-ord 4886  df-on 4887