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Mirrors > Home > ILE Home > Th. List > strslfv3 | Unicode version |
Description: Variant on strslfv 12381 for large structures. (Contributed by Mario Carneiro, 10-Jan-2017.) (Revised by Jim Kingdon, 30-Jan-2023.) |
Ref | Expression |
---|---|
strfv3.u | |
strfv3.s | Struct |
strslfv3.e | Slot |
strfv3.n | |
strfv3.c | |
strfv3.a |
Ref | Expression |
---|---|
strslfv3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | strfv3.a | . 2 | |
2 | strfv3.c | . . . 4 | |
3 | strfv3.s | . . . . 5 Struct | |
4 | strslfv3.e | . . . . 5 Slot | |
5 | strfv3.n | . . . . 5 | |
6 | 3, 4, 5 | strslfv 12381 | . . . 4 |
7 | 2, 6 | syl 14 | . . 3 |
8 | strfv3.u | . . . 4 | |
9 | 8 | fveq2d 5484 | . . 3 |
10 | 7, 9 | eqtr4d 2200 | . 2 |
11 | 1, 10 | eqtr4id 2216 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 wcel 2135 wss 3111 csn 3570 cop 3573 class class class wbr 3976 cfv 5182 cn 8848 Struct cstr 12333 cnx 12334 Slot cslot 12336 |
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 |
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-struct 12339 df-slot 12341 |
This theorem is referenced by: (None) |
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