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Mirrors > Home > MPE Home > Th. List > tskss | Structured version Unicode version |
Description: The subsets of an element of a Tarski class belong to the class. (Contributed by FL, 30-Dec-2010.) (Revised by Mario Carneiro, 18-Jun-2013.) |
Ref | Expression |
---|---|
tskss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elpw2g 4566 |
. . . 4
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2 | 1 | adantl 466 |
. . 3
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3 | tskpwss 9034 |
. . . 4
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4 | 3 | sseld 3466 |
. . 3
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5 | 2, 4 | sylbird 235 |
. 2
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6 | 5 | 3impia 1185 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 ax-sep 4524 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ral 2804 df-rex 2805 df-rab 2808 df-v 3080 df-dif 3442 df-un 3444 df-in 3446 df-ss 3453 df-nul 3749 df-if 3903 df-pw 3973 df-sn 3989 df-pr 3991 df-op 3995 df-br 4404 df-tsk 9031 |
This theorem is referenced by: tskin 9041 tsksn 9042 tsksuc 9044 tsk0 9045 tskr1om2 9050 tskint 9067 |
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