![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > tsetndx | Structured version Visualization version GIF version |
Description: Index value of the df-tset 16324 slot. (Contributed by Mario Carneiro, 14-Aug-2015.) |
Ref | Expression |
---|---|
tsetndx | ⊢ (TopSet‘ndx) = 9 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-tset 16324 | . 2 ⊢ TopSet = Slot 9 | |
2 | 9nn 11455 | . 2 ⊢ 9 ∈ ℕ | |
3 | 1, 2 | ndxarg 16247 | 1 ⊢ (TopSet‘ndx) = 9 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1658 ‘cfv 6123 9c9 11413 ndxcnx 16219 TopSetcts 16311 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1896 ax-4 1910 ax-5 2011 ax-6 2077 ax-7 2114 ax-8 2168 ax-9 2175 ax-10 2194 ax-11 2209 ax-12 2222 ax-13 2391 ax-ext 2803 ax-sep 5005 ax-nul 5013 ax-pow 5065 ax-pr 5127 ax-un 7209 ax-cnex 10308 ax-1cn 10310 ax-addcl 10312 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 881 df-3or 1114 df-3an 1115 df-tru 1662 df-ex 1881 df-nf 1885 df-sb 2070 df-mo 2605 df-eu 2640 df-clab 2812 df-cleq 2818 df-clel 2821 df-nfc 2958 df-ne 3000 df-ral 3122 df-rex 3123 df-reu 3124 df-rab 3126 df-v 3416 df-sbc 3663 df-csb 3758 df-dif 3801 df-un 3803 df-in 3805 df-ss 3812 df-pss 3814 df-nul 4145 df-if 4307 df-pw 4380 df-sn 4398 df-pr 4400 df-tp 4402 df-op 4404 df-uni 4659 df-iun 4742 df-br 4874 df-opab 4936 df-mpt 4953 df-tr 4976 df-id 5250 df-eprel 5255 df-po 5263 df-so 5264 df-fr 5301 df-we 5303 df-xp 5348 df-rel 5349 df-cnv 5350 df-co 5351 df-dm 5352 df-rn 5353 df-res 5354 df-ima 5355 df-pred 5920 df-ord 5966 df-on 5967 df-lim 5968 df-suc 5969 df-iota 6086 df-fun 6125 df-fn 6126 df-f 6127 df-f1 6128 df-fo 6129 df-f1o 6130 df-fv 6131 df-ov 6908 df-om 7327 df-wrecs 7672 df-recs 7734 df-rdg 7772 df-nn 11351 df-2 11414 df-3 11415 df-4 11416 df-5 11417 df-6 11418 df-7 11419 df-8 11420 df-9 11421 df-ndx 16225 df-slot 16226 df-tset 16324 |
This theorem is referenced by: topgrpstr 16401 otpsstr 16408 odrngstr 16419 imasvalstr 16465 ipostr 17506 psrvalstr 19724 cnfldstr 20108 cnfldfun 20118 indistpsx 21185 tuslem 22441 setsmsbas 22650 setsmsds 22651 tnglem 22814 tngds 22822 zlmtset 30554 |
Copyright terms: Public domain | W3C validator |