Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > strslfv | Unicode version |
Description: Extract a structure component (such as the base set) from a structure with a component extractor (such as the base set extractor df-base 11954). By virtue of ndxslid 11973, this can be done without having to refer to the hard-coded numeric index of . (Contributed by Mario Carneiro, 6-Oct-2013.) (Revised by Jim Kingdon, 30-Jan-2023.) |
Ref | Expression |
---|---|
strfv.s | Struct |
strslfv.e | Slot |
strfv.n |
Ref | Expression |
---|---|
strslfv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | strslfv.e | . 2 Slot | |
2 | strfv.s | . . 3 Struct | |
3 | structex 11960 | . . 3 Struct | |
4 | 2, 3 | mp1i 10 | . 2 |
5 | 2 | structfun 11966 | . . 3 |
6 | 5 | a1i 9 | . 2 |
7 | strfv.n | . . 3 | |
8 | 1 | simpri 112 | . . . . 5 |
9 | opexg 4145 | . . . . 5 | |
10 | 8, 9 | mpan 420 | . . . 4 |
11 | snssg 3651 | . . . 4 | |
12 | 10, 11 | syl 14 | . . 3 |
13 | 7, 12 | mpbiri 167 | . 2 |
14 | id 19 | . 2 | |
15 | 1, 4, 6, 13, 14 | strslfv2d 11990 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 cvv 2681 wss 3066 csn 3522 cop 3525 class class class wbr 3924 ccnv 4533 wfun 5112 cfv 5118 cn 8713 Struct cstr 11944 cnx 11945 Slot cslot 11947 |
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-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-un 4350 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ne 2307 df-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-sbc 2905 df-dif 3068 df-un 3070 df-in 3072 df-ss 3079 df-nul 3359 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-mpt 3986 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-res 4546 df-iota 5083 df-fun 5120 df-fv 5126 df-struct 11950 df-slot 11952 |
This theorem is referenced by: strslfv3 11993 |
Copyright terms: Public domain | W3C validator |