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Theorem tskpw 9152
Description: Second axiom of a Tarski class. The powerset of an element of a Tarski class belongs to the class. (Contributed by FL, 30-Dec-2010.) (Proof shortened by Mario Carneiro, 20-Sep-2014.)
Assertion
Ref Expression
tskpw

Proof of Theorem tskpw
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eltsk2g 9150 . . . . 5
21ibi 241 . . . 4
32simpld 459 . . 3
4 simpr 461 . . . 4
54ralimi 2850 . . 3
63, 5syl 16 . 2
7 pweq 4015 . . . 4
87eleq1d 2526 . . 3
98rspccva 3209 . 2
106, 9sylan 471 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  \/wo 368  /\wa 369  =wceq 1395  e.wcel 1818  A.wral 2807  C_wss 3475  ~Pcpw 4012   class class class wbr 4452   cen 7533   ctsk 9147
This theorem is referenced by:  tsksn  9159  tsksuc  9161  tskr1om  9166  inttsk  9173  tskcard  9180  tskwun  9183  grutsk1  9220  pwinfi3  37748
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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