Theorem eltsk2g 9150

Description: Properties of a Tarski class. (Contributed by FL, 30-Dec-2010.) (Revised by Mario Carneiro, 20-Sep-2014.)

Assertion

Ref	Expression
eltsk2g

Distinct variable group:   ,

Proof of Theorem eltsk2g

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		eltskg 9149	. 2
2		nfra1 2838	. . . . . . 7
3		pweq 4015	. . . . . . . . . . . 12
4	3	sseq1d 3530	. . . . . . . . . . 11
5	4	rspccva 3209	. . . . . . . . . 10
6	5	adantlr 714	. . . . . . . . 9
7		vex 3112	. . . . . . . . . . . 12
8	7	pwex 4635	. . . . . . . . . . 11
9	8	elpw 4018	. . . . . . . . . 10
10		ssel 3497	. . . . . . . . . 10
11	9, 10	syl5bir 218	. . . . . . . . 9
12	6, 11	syl 16	. . . . . . . 8
13	12	rexlimdva 2949	. . . . . . 7
14	2, 13	ralimdaa 2859	. . . . . 6
15	14	imdistani 690	. . . . 5
16		r19.26 2984	. . . . 5
17		r19.26 2984	. . . . 5
18	15, 16, 17	3imtr4i 266	. . . 4
19		ssid 3522	. . . . . . 7
20		sseq2 3525	. . . . . . . 8
21	20	rspcev 3210	. . . . . . 7
22	19, 21	mpan2 671	. . . . . 6
23	22	anim2i 569	. . . . 5
24	23	ralimi 2850	. . . 4
25	18, 24	impbii 188	. . 3
26	25	anbi1i 695	. 2
27	1, 26	syl6bb 261	1

Syntax hints:  ->wi 4  <->wb 184  \/wo 368  /\wa 369  e.wcel 1818  A.wral 2807  E.wrex 2808  C_wss 3475  ~Pcpw 4012   class class class wbr 4452  cen 7533  ctsk 9147

This theorem is referenced by:  tskpw  9152  0tsk  9154  inttsk  9173  inatsk  9177

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