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Mirrors > Home > MPE Home > Th. List > basendxnn | Structured version Visualization version GIF version |
Description: The index value of the base set extractor is a positive integer. This property should be ensured for every concrete coding because otherwise it could not be used in an extensible structure (slots must be positive integers). (Contributed by AV, 23-Sep-2020.) (Proof shortened by AV, 13-Oct-2024.) |
Ref | Expression |
---|---|
basendxnn | ⊢ (Base‘ndx) ∈ ℕ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | basendx 17222 | . 2 ⊢ (Base‘ndx) = 1 | |
2 | 1nn 12275 | . 2 ⊢ 1 ∈ ℕ | |
3 | 1, 2 | eqeltri 2822 | 1 ⊢ (Base‘ndx) ∈ ℕ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2099 ‘cfv 6554 1c1 11159 ℕcn 12264 ndxcnx 17195 Basecbs 17213 |
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 2697 ax-sep 5304 ax-nul 5311 ax-pow 5369 ax-pr 5433 ax-un 7746 ax-cnex 11214 ax-1cn 11216 ax-addcl 11218 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3or 1085 df-3an 1086 df-tru 1537 df-fal 1547 df-ex 1775 df-nf 1779 df-sb 2061 df-mo 2529 df-eu 2558 df-clab 2704 df-cleq 2718 df-clel 2803 df-nfc 2878 df-ne 2931 df-ral 3052 df-rex 3061 df-reu 3365 df-rab 3420 df-v 3464 df-sbc 3777 df-csb 3893 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-pss 3967 df-nul 4326 df-if 4534 df-pw 4609 df-sn 4634 df-pr 4636 df-op 4640 df-uni 4914 df-iun 5003 df-br 5154 df-opab 5216 df-mpt 5237 df-tr 5271 df-id 5580 df-eprel 5586 df-po 5594 df-so 5595 df-fr 5637 df-we 5639 df-xp 5688 df-rel 5689 df-cnv 5690 df-co 5691 df-dm 5692 df-rn 5693 df-res 5694 df-ima 5695 df-pred 6312 df-ord 6379 df-on 6380 df-lim 6381 df-suc 6382 df-iota 6506 df-fun 6556 df-fn 6557 df-f 6558 df-f1 6559 df-fo 6560 df-f1o 6561 df-fv 6562 df-ov 7427 df-om 7877 df-2nd 8004 df-frecs 8296 df-wrecs 8327 df-recs 8401 df-rdg 8440 df-nn 12265 df-slot 17184 df-ndx 17196 df-base 17214 |
This theorem is referenced by: 1strstr1 17229 2strstr1 17238 basendxnplusgndx 17296 tsetndxnbasendx 17370 plendxnbasendx 17384 dsndxnbasendx 17403 unifndxnbasendx 17413 basendxnedgfndx 28931 structvtxvallem 28956 |
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