Theorem tsksn 9159

Description: A singleton of an element of a Tarski class belongs to the class. JFM CLASSES2 th. 2 (partly). (Contributed by FL, 22-Feb-2011.) (Revised by Mario Carneiro, 18-Jun-2013.)

Assertion

Ref	Expression
tsksn

Proof of Theorem tsksn

Step	Hyp	Ref	Expression
1		tskpw 9152	. 2
2		snsspw 4201	. . 3
3		tskss 9157	. . 3
4	2, 3	mp3an3 1313	. 2
5	1, 4	syldan 470	1

Syntax hints:  ->wi 4  /\wa 369  e.wcel 1818  C_wss 3475  ~Pcpw 4012  {csn 4029  ctsk 9147

This theorem is referenced by:  tsk1  9163  tskop  9170

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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-pow 4630

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