![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
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 12042. (Contributed by Jim Kingdon, 29-Jan-2023.) |
Ref | Expression |
---|---|
ndxarg.1 |
![]() ![]() ![]() ![]() |
ndxarg.2 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
ndxslid |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ndxarg.1 |
. . 3
![]() ![]() ![]() ![]() | |
2 | ndxarg.2 |
. . 3
![]() ![]() ![]() ![]() | |
3 | 1, 2 | ndxid 12022 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | 1, 2 | ndxarg 12021 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | 4, 2 | eqeltri 2213 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | 3, 5 | pm3.2i 270 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-un 4363 ax-cnex 7735 ax-resscn 7736 ax-1re 7738 ax-addrcl 7741 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-sbc 2914 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-int 3780 df-br 3938 df-opab 3998 df-mpt 3999 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-res 4559 df-iota 5096 df-fun 5133 df-fv 5139 df-inn 8745 df-ndx 12001 df-slot 12002 |
This theorem is referenced by: base0 12047 baseslid 12054 plusgslid 12093 2stropg 12100 2strop1g 12103 mulrslid 12110 starvslid 12119 scaslid 12127 vscaslid 12130 ipslid 12138 tsetslid 12148 pleslid 12155 dsslid 12158 |
Copyright terms: Public domain | W3C validator |