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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-base 12343 | . . 3 Slot | |
2 | 1nn 8859 | . . 3 | |
3 | 1, 2 | ndxarg 12360 | . 2 |
4 | 3, 2 | eqeltri 2237 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2135 cfv 5182 c1 7745 cn 8848 cnx 12334 cbs 12337 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-un 4405 ax-cnex 7835 ax-resscn 7836 ax-1re 7838 ax-addrcl 7841 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-sbc 2947 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-int 3819 df-br 3977 df-opab 4038 df-mpt 4039 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-rn 4609 df-res 4610 df-iota 5147 df-fun 5184 df-fv 5190 df-inn 8849 df-ndx 12340 df-slot 12341 df-base 12343 |
This theorem is referenced by: baseslid 12393 ressval2 12397 ressid 12398 1strbas 12436 2strbasg 12438 2stropg 12439 2strbas1g 12441 rngbaseg 12453 srngbased 12460 lmodbased 12471 ipsbased 12479 topgrpbasd 12489 |
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