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Mirrors > Home > ILE Home > Th. List > setsslnid | Unicode version |
Description: Value of the structure replacement function at an untouched index. (Contributed by Mario Carneiro, 1-Dec-2014.) (Revised by Jim Kingdon, 24-Jan-2023.) |
Ref | Expression |
---|---|
setsslid.e | Slot |
setsslnid.n | |
setsslnid.d |
Ref | Expression |
---|---|
setsslnid | sSet |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | setsslnid.d | . . . . 5 | |
2 | setsresg 12369 | . . . . 5 sSet | |
3 | 1, 2 | mp3an2 1314 | . . . 4 sSet |
4 | 3 | fveq1d 5482 | . . 3 sSet |
5 | setsslid.e | . . . . . . 7 Slot | |
6 | 5 | simpri 112 | . . . . . 6 |
7 | 6 | elexi 2733 | . . . . 5 |
8 | setsslnid.n | . . . . 5 | |
9 | eldifsn 3697 | . . . . 5 | |
10 | 7, 8, 9 | mpbir2an 931 | . . . 4 |
11 | fvres 5504 | . . . 4 sSet sSet | |
12 | 10, 11 | ax-mp 5 | . . 3 sSet sSet |
13 | fvres 5504 | . . . 4 | |
14 | 10, 13 | ax-mp 5 | . . 3 |
15 | 4, 12, 14 | 3eqtr3g 2220 | . 2 sSet |
16 | 5 | simpli 110 | . . 3 Slot |
17 | setsex 12363 | . . . 4 sSet | |
18 | 1, 17 | mp3an2 1314 | . . 3 sSet |
19 | 6 | a1i 9 | . . 3 |
20 | 16, 18, 19 | strnfvnd 12351 | . 2 sSet sSet |
21 | simpl 108 | . . 3 | |
22 | 16, 21, 19 | strnfvnd 12351 | . 2 |
23 | 15, 20, 22 | 3eqtr4rd 2208 | 1 sSet |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 wcel 2135 wne 2334 cvv 2721 cdif 3108 csn 3570 cop 3573 cres 4600 cfv 5182 (class class class)co 5836 cn 8848 cnx 12328 sSet csts 12329 Slot cslot 12330 |
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 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-un 4405 ax-setind 4508 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2723 df-sbc 2947 df-dif 3113 df-un 3115 df-in 3117 df-ss 3124 df-nul 3405 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-mpt 4039 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-rn 4609 df-res 4610 df-iota 5147 df-fun 5184 df-fv 5190 df-ov 5839 df-oprab 5840 df-mpo 5841 df-slot 12335 df-sets 12338 |
This theorem is referenced by: setsmsbasg 13020 setsmsdsg 13021 |
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