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Mirrors > Home > ILE Home > Th. List > basendxnn | Unicode 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.) |
Ref | Expression |
---|---|
basendxnn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-base 12448 |
. . 3
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2 | 1nn 8916 |
. . 3
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3 | 1, 2 | ndxarg 12465 |
. 2
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4 | 3, 2 | eqeltri 2250 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4206 ax-un 4430 ax-cnex 7890 ax-resscn 7891 ax-1re 7893 ax-addrcl 7896 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-sbc 2963 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-int 3843 df-br 4001 df-opab 4062 df-mpt 4063 df-id 4290 df-xp 4629 df-rel 4630 df-cnv 4631 df-co 4632 df-dm 4633 df-rn 4634 df-res 4635 df-iota 5174 df-fun 5214 df-fv 5220 df-inn 8906 df-ndx 12445 df-slot 12446 df-base 12448 |
This theorem is referenced by: baseslid 12498 ressvalsets 12503 ressex 12504 resseqnbasd 12511 ressressg 12513 1strbas 12552 2strbasg 12554 2stropg 12555 2strbas1g 12557 rngbaseg 12570 srngbased 12577 lmodbased 12591 ipsbased 12599 tsetndxnbasendx 12610 topgrpbasd 12616 dsndxnbasendx 12627 ring1 13059 |
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