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Theorem tskpwss 9131
 Description: First axiom of a Tarski class. The subsets of an element of a Tarski 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 9129 . . . . 5
21ibi 241 . . . 4
32simpld 459 . . 3
4 simpl 457 . . . 4
54ralimi 2857 . . 3
63, 5syl 16 . 2
7 pweq 4013 . . . 4
87sseq1d 3531 . . 3
98rspccva 3213 . 2
106, 9sylan 471 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wo 368   wa 369   wceq 1379   wcel 1767  wral 2814  wrex 2815   wss 3476  cpw 4010   class class class wbr 4447   cen 7514  ctsk 9127 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-pw 4012  df-sn 4028  df-pr 4030  df-op 4034  df-br 4448  df-tsk 9128 This theorem is referenced by:  tsksdom  9135  tskss  9137  tsktrss  9140  inttsk  9153  tskcard  9160
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