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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.
StepHypRef Expression
1 eltskg 9149 . 2
2 nfra1 2838 . . . . . . 7
3 pweq 4015 . . . . . . . . . . . 12
43sseq1d 3530 . . . . . . . . . . 11
54rspccva 3209 . . . . . . . . . 10
65adantlr 714 . . . . . . . . 9
7 vex 3112 . . . . . . . . . . . 12
87pwex 4635 . . . . . . . . . . 11
98elpw 4018 . . . . . . . . . 10
10 ssel 3497 . . . . . . . . . 10
119, 10syl5bir 218 . . . . . . . . 9
126, 11syl 16 . . . . . . . 8
1312rexlimdva 2949 . . . . . . 7
142, 13ralimdaa 2859 . . . . . 6
1514imdistani 690 . . . . 5
16 r19.26 2984 . . . . 5
17 r19.26 2984 . . . . 5
1815, 16, 173imtr4i 266 . . . 4
19 ssid 3522 . . . . . . 7
20 sseq2 3525 . . . . . . . 8
2120rspcev 3210 . . . . . . 7
2219, 21mpan2 671 . . . . . 6
2322anim2i 569 . . . . 5
2423ralimi 2850 . . . 4
2518, 24impbii 188 . . 3
2625anbi1i 695 . 2
271, 26syl6bb 261 1
 Colors of variables: wff setvar class 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
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