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Theorem tskpwss 8632
 Description: 1st axiom of a Tarski's class. The subsets of an element of a Tarski's class belong to the class. (Contributed by FL, 30-Dec-2010.) (Proof shortened by Mario Carneiro, 20-Sep-2014.)
Assertion
Ref Expression
tskpwss

Proof of Theorem tskpwss
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eltskg 8630 . . . . 5
21ibi 234 . . . 4
32simpld 447 . . 3
4 simpl 445 . . . 4
54ralimi 2783 . . 3
63, 5syl 16 . 2
7 pweq 3804 . . . 4
87sseq1d 3377 . . 3
98rspccva 3053 . 2
106, 9sylan 459 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 359   wa 360   wceq 1653   wcel 1726  wral 2707  wrex 2708   wss 3322  cpw 3801   class class class wbr 4215   cen 7109  ctsk 8628 This theorem is referenced by:  tsksdom  8636  tskss  8638  tsktrss  8641  inttsk  8654  tskcard  8661 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 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 4216  df-tsk 8629
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