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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 12520. (Contributed by Jim Kingdon, 29-Jan-2023.) |
Ref | Expression |
---|---|
ndxarg.1 |
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ndxarg.2 |
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Ref | Expression |
---|---|
ndxslid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ndxarg.1 |
. . 3
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2 | ndxarg.2 |
. . 3
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3 | 1, 2 | ndxid 12499 |
. 2
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4 | 1, 2 | ndxarg 12498 |
. . 3
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5 | 4, 2 | eqeltri 2260 |
. 2
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6 | 3, 5 | pm3.2i 272 |
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 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-13 2160 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-pow 4186 ax-pr 4221 ax-un 4445 ax-cnex 7915 ax-resscn 7916 ax-1re 7918 ax-addrcl 7921 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-rex 2471 df-v 2751 df-sbc 2975 df-un 3145 df-in 3147 df-ss 3154 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-int 3857 df-br 4016 df-opab 4077 df-mpt 4078 df-id 4305 df-xp 4644 df-rel 4645 df-cnv 4646 df-co 4647 df-dm 4648 df-rn 4649 df-res 4650 df-iota 5190 df-fun 5230 df-fv 5236 df-inn 8933 df-ndx 12478 df-slot 12479 |
This theorem is referenced by: base0 12525 baseslid 12532 plusgslid 12585 2stropg 12593 2strop1g 12596 mulrslid 12604 starvslid 12613 scaslid 12625 vscaslid 12635 ipslid 12643 tsetslid 12660 pleslid 12674 dsslid 12685 homslid 12702 ccoslid 12704 zlmlemg 13761 |
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