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Theorem eltsk2g 8628
 Description: Properties of a Tarski's class. (Contributed by FL, 30-Dec-2010.) (Revised by Mario Carneiro, 20-Sep-2014.)
Assertion
Ref Expression
eltsk2g
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem eltsk2g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eltskg 8627 . 2
2 nfra1 2758 . . . . . . 7
3 pweq 3804 . . . . . . . . . . . 12
43sseq1d 3377 . . . . . . . . . . 11
54rspccva 3053 . . . . . . . . . 10
65adantlr 697 . . . . . . . . 9
7 vex 2961 . . . . . . . . . . . 12
87pwex 4384 . . . . . . . . . . 11
98elpw 3807 . . . . . . . . . 10
10 ssel 3344 . . . . . . . . . 10
119, 10syl5bir 211 . . . . . . . . 9
126, 11syl 16 . . . . . . . 8
1312rexlimdva 2832 . . . . . . 7
142, 13ralimdaa 2785 . . . . . 6
1514imdistani 673 . . . . 5
16 r19.26 2840 . . . . 5
17 r19.26 2840 . . . . 5
1815, 16, 173imtr4i 259 . . . 4
19 ssid 3369 . . . . . . 7
20 sseq2 3372 . . . . . . . 8
2120rspcev 3054 . . . . . . 7
2219, 21mpan2 654 . . . . . 6
2322anim2i 554 . . . . 5
2423ralimi 2783 . . . 4
2518, 24impbii 182 . . 3
2625anbi1i 678 . 2
271, 26syl6bb 254 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wo 359   wa 360   wcel 1726  wral 2707  wrex 2708   wss 3322  cpw 3801   class class class wbr 4214   cen 7108  ctsk 8625 This theorem is referenced by:  tskpw  8630  0tsk  8632  inttsk  8651  inatsk  8655 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-pow 4379 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-op 3825  df-br 4215  df-tsk 8626
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