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Theorem eltskg 8625
 Description: Properties of a Tarski's class. (Contributed by FL, 30-Dec-2010.)
Assertion
Ref Expression
eltskg
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem eltskg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sseq2 3370 . . . . 5
2 rexeq 2905 . . . . 5
31, 2anbi12d 692 . . . 4
43raleqbi1dv 2912 . . 3
5 pweq 3802 . . . 4
6 breq2 4216 . . . . 5
7 eleq2 2497 . . . . 5
86, 7orbi12d 691 . . . 4
95, 8raleqbidv 2916 . . 3
104, 9anbi12d 692 . 2
11 df-tsk 8624 . 2
1210, 11elab2g 3084 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wo 358   wa 359   wceq 1652   wcel 1725  wral 2705  wrex 2706   wss 3320  cpw 3799   class class class wbr 4212   cen 7106  ctsk 8623 This theorem is referenced by:  eltsk2g  8626  tskpwss  8627  tsken  8629  grothtsk  8710 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-pw 3801  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-tsk 8624
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