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Mirrors > Home > ILE Home > Th. List > ndxslid | Unicode version |
Description: A structure component extractor is defined by its own index. That the index is a natural number will also be needed in quite a few contexts so it is included in the conclusion of this theorem which can be used as a hypothesis of theorems like strslfv 12447. (Contributed by Jim Kingdon, 29-Jan-2023.) |
Ref | Expression |
---|---|
ndxarg.1 | Slot |
ndxarg.2 |
Ref | Expression |
---|---|
ndxslid | Slot |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ndxarg.1 | . . 3 Slot | |
2 | ndxarg.2 | . . 3 | |
3 | 1, 2 | ndxid 12427 | . 2 Slot |
4 | 1, 2 | ndxarg 12426 | . . 3 |
5 | 4, 2 | eqeltri 2243 | . 2 |
6 | 3, 5 | pm3.2i 270 | 1 Slot |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1348 wcel 2141 cfv 5196 cn 8865 cnx 12400 Slot cslot 12402 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-pr 4192 ax-un 4416 ax-cnex 7852 ax-resscn 7853 ax-1re 7855 ax-addrcl 7858 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-sbc 2956 df-un 3125 df-in 3127 df-ss 3134 df-pw 3566 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-int 3830 df-br 3988 df-opab 4049 df-mpt 4050 df-id 4276 df-xp 4615 df-rel 4616 df-cnv 4617 df-co 4618 df-dm 4619 df-rn 4620 df-res 4621 df-iota 5158 df-fun 5198 df-fv 5204 df-inn 8866 df-ndx 12406 df-slot 12407 |
This theorem is referenced by: base0 12452 baseslid 12459 plusgslid 12500 2stropg 12507 2strop1g 12510 mulrslid 12517 starvslid 12526 scaslid 12534 vscaslid 12537 ipslid 12545 tsetslid 12555 pleslid 12562 dsslid 12565 |
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