tsetndx - Metamath Proof Explorer

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Theorem tsetndx 17333

Description: Index value of the df-tset 17252 slot. (Contributed by Mario Carneiro, 14-Aug-2015.) (New usage is discouraged.)

**Assertion**
Ref	Expression
tsetndx	⊢ (TopSet‘ndx) = 9

**Proof of Theorem tsetndx**
Step	Hyp	Ref	Expression
1		df-tset 17252	. 2 ⊢ TopSet = Slot 9
2		9nn 12341	. 2 ⊢ 9 ∈ ℕ
3	1, 2	ndxarg 17165	1 ⊢ (TopSet‘ndx) = 9

Colors of variables: wff setvar class

Syntax hints: = wceq 1534 ‘cfv 6548 9c9 12305 ndxcnx 17162 TopSetcts 17239

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-10 2130 ax-11 2147 ax-12 2167 ax-ext 2699 ax-sep 5299 ax-nul 5306 ax-pow 5365 ax-pr 5429 ax-un 7740 ax-cnex 11195 ax-1cn 11197 ax-addcl 11199

This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-3or 1086 df-3an 1087 df-tru 1537 df-fal 1547 df-ex 1775 df-nf 1779 df-sb 2061 df-mo 2530 df-eu 2559 df-clab 2706 df-cleq 2720 df-clel 2806 df-nfc 2881 df-ne 2938 df-ral 3059 df-rex 3068 df-reu 3374 df-rab 3430 df-v 3473 df-sbc 3777 df-csb 3893 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-pss 3966 df-nul 4324 df-if 4530 df-pw 4605 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4909 df-iun 4998 df-br 5149 df-opab 5211 df-mpt 5232 df-tr 5266 df-id 5576 df-eprel 5582 df-po 5590 df-so 5591 df-fr 5633 df-we 5635 df-xp 5684 df-rel 5685 df-cnv 5686 df-co 5687 df-dm 5688 df-rn 5689 df-res 5690 df-ima 5691 df-pred 6305 df-ord 6372 df-on 6373 df-lim 6374 df-suc 6375 df-iota 6500 df-fun 6550 df-fn 6551 df-f 6552 df-f1 6553 df-fo 6554 df-f1o 6555 df-fv 6556 df-ov 7423 df-om 7871 df-2nd 7994 df-frecs 8287 df-wrecs 8318 df-recs 8392 df-rdg 8431 df-nn 12244 df-2 12306 df-3 12307 df-4 12308 df-5 12309 df-6 12310 df-7 12311 df-8 12312 df-9 12313 df-slot 17151 df-ndx 17163 df-tset 17252

This theorem is referenced by: tsetndxnn 17335 basendxlttsetndx 17336 tsetndxnplusgndx 17338 tsetndxnmulrndx 17339 tsetndxnstarvndx 17340 slotstnscsi 17341 topgrpstr 17342 slotsdifplendx 17356 otpsstr 17357 dsndxntsetndx 17374 unifndxntsetndx 17381 odrngstr 17384 imasvalstr 17433 ipostr 18521 symgvalstructOLD 19352 cnfldstr 21281 cnfldstrOLD 21296 cnfldfunALTOLDOLD 21308 psrvalstr 21849 indistpsx 22926 tuslemOLD 24185 setsmsbasOLD 24395 setsmsdsOLD 24397 tnglemOLD 24563 tngdsOLD 24578 idlsrgstr 33226 zlmtsetOLD 33566

	
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