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 11970). By virtue of ndxslid 11989, 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 11976 | . . 3 Struct | |
4 | 2, 3 | mp1i 10 | . 2 |
5 | 2 | structfun 11982 | . . 3 |
6 | 5 | a1i 9 | . 2 |
7 | strfv.n | . . 3 | |
8 | 1 | simpri 112 | . . . . 5 |
9 | opexg 4150 | . . . . 5 | |
10 | 8, 9 | mpan 420 | . . . 4 |
11 | snssg 3656 | . . . 4 | |
12 | 10, 11 | syl 14 | . . 3 |
13 | 7, 12 | mpbiri 167 | . 2 |
14 | id 19 | . 2 | |
15 | 1, 4, 6, 13, 14 | strslfv2d 12006 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 cvv 2686 wss 3071 csn 3527 cop 3530 class class class wbr 3929 ccnv 4538 wfun 5117 cfv 5123 cn 8725 Struct cstr 11960 cnx 11961 Slot cslot 11963 |
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 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 |
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 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ne 2309 df-ral 2421 df-rex 2422 df-rab 2425 df-v 2688 df-sbc 2910 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-nul 3364 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-mpt 3991 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-res 4551 df-iota 5088 df-fun 5125 df-fv 5131 df-struct 11966 df-slot 11968 |
This theorem is referenced by: strslfv3 12009 |
Copyright terms: Public domain | W3C validator |