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Mirrors > Home > MPE Home > Th. List > tskmid | Structured version Visualization version GIF version |
Description: The set π΄ is an element of the smallest Tarski class that contains π΄. CLASSES1 th. 5. (Contributed by FL, 30-Dec-2010.) (Proof shortened by Mario Carneiro, 21-Sep-2014.) |
Ref | Expression |
---|---|
tskmid | β’ (π΄ β π β π΄ β (tarskiMapβπ΄)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . . . 4 β’ (π΄ β π₯ β π΄ β π₯) | |
2 | 1 | rgenw 3063 | . . 3 β’ βπ₯ β Tarski (π΄ β π₯ β π΄ β π₯) |
3 | elintrabg 4964 | . . 3 β’ (π΄ β π β (π΄ β β© {π₯ β Tarski β£ π΄ β π₯} β βπ₯ β Tarski (π΄ β π₯ β π΄ β π₯))) | |
4 | 2, 3 | mpbiri 257 | . 2 β’ (π΄ β π β π΄ β β© {π₯ β Tarski β£ π΄ β π₯}) |
5 | tskmval 10836 | . 2 β’ (π΄ β π β (tarskiMapβπ΄) = β© {π₯ β Tarski β£ π΄ β π₯}) | |
6 | 4, 5 | eleqtrrd 2834 | 1 β’ (π΄ β π β π΄ β (tarskiMapβπ΄)) |
Colors of variables: wff setvar class |
Syntax hints: β wi 4 β wcel 2104 βwral 3059 {crab 3430 β© cint 4949 βcfv 6542 Tarskictsk 10745 tarskiMapctskm 10834 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1911 ax-6 1969 ax-7 2009 ax-8 2106 ax-9 2114 ax-10 2135 ax-11 2152 ax-12 2169 ax-ext 2701 ax-sep 5298 ax-nul 5305 ax-pr 5426 ax-groth 10820 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 844 df-3an 1087 df-tru 1542 df-fal 1552 df-ex 1780 df-nf 1784 df-sb 2066 df-mo 2532 df-eu 2561 df-clab 2708 df-cleq 2722 df-clel 2808 df-nfc 2883 df-ne 2939 df-ral 3060 df-rex 3069 df-rab 3431 df-v 3474 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-nul 4322 df-if 4528 df-pw 4603 df-sn 4628 df-pr 4630 df-op 4634 df-uni 4908 df-int 4950 df-br 5148 df-opab 5210 df-mpt 5231 df-id 5573 df-xp 5681 df-rel 5682 df-cnv 5683 df-co 5684 df-dm 5685 df-iota 6494 df-fun 6544 df-fv 6550 df-tsk 10746 df-tskm 10835 |
This theorem is referenced by: eltskm 10840 |
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