Theorem tskss 9157

Description: The subsets of an element of a Tarski class belong to the class. (Contributed by FL, 30-Dec-2010.) (Revised by Mario Carneiro, 18-Jun-2013.)

Assertion

Ref	Expression
tskss

Proof of Theorem tskss

Step	Hyp	Ref	Expression
1		elpw2g 4615	. . . 4
2	1	adantl 466	. . 3
3		tskpwss 9151	. . . 4
4	3	sseld 3502	. . 3
5	2, 4	sylbird 235	. 2
6	5	3impia 1193	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  e.wcel 1818  C_wss 3475  ~Pcpw 4012  ctsk 9147

This theorem is referenced by:  tskin  9158  tsksn  9159  tsksuc  9161  tsk0  9162  tskr1om2  9167  tskint  9184

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-tsk 9148