Theorem tskssel 9156

Description: A part of a Tarski class strictly dominated by the class is an element of the class. JFM CLASSES2 th. 2. (Contributed by FL, 22-Feb-2011.) (Proof shortened by Mario Carneiro, 20-Sep-2014.)

Assertion

Ref	Expression
tskssel

Proof of Theorem tskssel

Step	Hyp	Ref	Expression
1		sdomnen 7564	. . 3
2	1	3ad2ant3 1019	. 2
3		tsken 9153	. . . 4
4	3	3adant3 1016	. . 3
5	4	ord 377	. 2
6	2, 5	mpd 15	1

Syntax hints:  -.wn 3  ->wi 4  \/wo 368  /\w3a 973  e.wcel 1818  C_wss 3475   class class class wbr 4452  cen 7533  csdm 7535  ctsk 9147

This theorem is referenced by:  tskpr  9169  tskwe2  9172  tskord  9179  tskcard  9180  tskurn  9188

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  ax-sep 4573

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  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-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-pw 4014  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-sdom 7539  df-tsk 9148