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Mirrors > Home > MPE Home > Th. List > tsetid | Structured version Visualization version GIF version |
Description: Utility theorem: index-independent form of df-tset 17223. (Contributed by NM, 20-Oct-2012.) |
Ref | Expression |
---|---|
tsetid | ⊢ TopSet = Slot (TopSet‘ndx) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-tset 17223 | . 2 ⊢ TopSet = Slot 9 | |
2 | 9nn 12317 | . 2 ⊢ 9 ∈ ℕ | |
3 | 1, 2 | ndxid 17137 | 1 ⊢ TopSet = Slot (TopSet‘ndx) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1540 ‘cfv 6543 9c9 12281 Slot cslot 17121 ndxcnx 17133 TopSetcts 17210 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2153 ax-12 2170 ax-ext 2702 ax-sep 5299 ax-nul 5306 ax-pow 5363 ax-pr 5427 ax-un 7729 ax-cnex 11172 ax-1cn 11174 ax-addcl 11176 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-3or 1087 df-3an 1088 df-tru 1543 df-fal 1553 df-ex 1781 df-nf 1785 df-sb 2067 df-mo 2533 df-eu 2562 df-clab 2709 df-cleq 2723 df-clel 2809 df-nfc 2884 df-ne 2940 df-ral 3061 df-rex 3070 df-reu 3376 df-rab 3432 df-v 3475 df-sbc 3778 df-csb 3894 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-pss 3967 df-nul 4323 df-if 4529 df-pw 4604 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-iun 4999 df-br 5149 df-opab 5211 df-mpt 5232 df-tr 5266 df-id 5574 df-eprel 5580 df-po 5588 df-so 5589 df-fr 5631 df-we 5633 df-xp 5682 df-rel 5683 df-cnv 5684 df-co 5685 df-dm 5686 df-rn 5687 df-res 5688 df-ima 5689 df-pred 6300 df-ord 6367 df-on 6368 df-lim 6369 df-suc 6370 df-iota 6495 df-fun 6545 df-fn 6546 df-f 6547 df-f1 6548 df-fo 6549 df-f1o 6550 df-fv 6551 df-ov 7415 df-om 7860 df-2nd 7980 df-frecs 8272 df-wrecs 8303 df-recs 8377 df-rdg 8416 df-nn 12220 df-2 12282 df-3 12283 df-4 12284 df-5 12285 df-6 12286 df-7 12287 df-8 12288 df-9 12289 df-slot 17122 df-ndx 17134 df-tset 17223 |
This theorem is referenced by: topgrptset 17316 resstset 17317 otpstset 17330 odrngtset 17359 prdstset 17419 imastset 17475 ipotset 18496 oppgtset 19266 mgptset 20045 sratset 21036 cnfldtset 21240 eltpsg 22764 indistpsALT 22835 resstopn 23009 tuslem 24090 tuslemOLD 24091 setsmstset 24304 tngtset 24485 nrgtrg 24526 idlsrgtset 33061 zlmtset 33407 zlmtsetOLD 33408 gg-cnfldtset 35639 |
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