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Mirrors > Home > ILE Home > Th. List > ndxid | Unicode version |
Description: A structure component
extractor is defined by its own index. This
theorem, together with strslfv 12489 below, is useful for avoiding direct
reference to the hard-coded numeric index in component extractor
definitions, such as the ![]() (Contributed by NM, 19-Oct-2012.) (Revised by Mario Carneiro, 6-Oct-2013.) (Proof shortened by BJ, 27-Dec-2021.) |
Ref | Expression |
---|---|
ndxarg.1 |
![]() ![]() ![]() ![]() |
ndxarg.2 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
ndxid |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ndxarg.1 |
. . . 4
![]() ![]() ![]() ![]() | |
2 | ndxarg.2 |
. . . 4
![]() ![]() ![]() ![]() | |
3 | 1, 2 | ndxarg 12468 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | 3 | eqcomi 2181 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | sloteq 12450 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | 1, 5 | eqtrid 2222 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | 4, 6 | ax-mp 5 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 7893 ax-resscn 7894 ax-1re 7896 ax-addrcl 7899 |
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 8909 df-ndx 12448 df-slot 12449 |
This theorem is referenced by: ndxslid 12470 strndxid 12473 baseid 12498 plusgid 12550 mulrid 12568 starvid 12577 scaid 12585 vscaid 12591 ipid 12599 tsetid 12609 pleid 12623 dsid 12626 |
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