Theorem tsksuc 9161

Description: If an element of a Tarski class is an ordinal number, its successor is an element of the class. JFM CLASSES2 th. 6 (partly). (Contributed by FL, 22-Feb-2011.) (Proof shortened by Mario Carneiro, 20-Sep-2014.)

Assertion

Ref	Expression
tsksuc

Proof of Theorem tsksuc

Step	Hyp	Ref	Expression
1		simp1 996	. 2
2		tskpw 9152	. . 3
3	2	3adant2 1015	. 2
4		eloni 4893	. . . . 5
5	4	3ad2ant2 1018	. . . 4
6		ordunisuc 6667	. . . 4
7		eqimss 3555	. . . 4
8	5, 6, 7	3syl 20	. . 3
9		sspwuni 4416	. . 3
10	8, 9	sylibr 212	. 2
11		tskss 9157	. 2
12	1, 3, 10, 11	syl3anc 1228	1

Syntax hints:  ->wi 4  /\w3a 973  =wceq 1395  e.wcel 1818  C_wss 3475  ~Pcpw 4012  U.cuni 4249  Ordword 4882  con0 4883  succsuc 4885  ctsk 9147

This theorem is referenced by:  tsk2  9164

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-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pow 4630  ax-pr 4691  ax-un 6592

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-pss 3491  df-nul 3785  df-if 3942  df-pw 4014  df-sn 4030  df-pr 4032  df-tp 4034  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-tr 4546  df-eprel 4796  df-po 4805  df-so 4806  df-fr 4843  df-we 4845  df-ord 4886  df-on 4887  df-suc 4889  df-tsk 9148