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Mirrors > Home > ILE Home > Th. List > opelstrbas | GIF version |
Description: The base set of a structure with a base set. (Contributed by AV, 10-Nov-2021.) |
Ref | Expression |
---|---|
opelstrbas.s | β’ (π β π Struct π) |
opelstrbas.v | β’ (π β π β π) |
opelstrbas.b | β’ (π β β¨(Baseβndx), πβ© β π) |
Ref | Expression |
---|---|
opelstrbas | β’ (π β π = (Baseβπ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | baseslid 12522 | . 2 β’ (Base = Slot (Baseβndx) β§ (Baseβndx) β β) | |
2 | opelstrbas.s | . 2 β’ (π β π Struct π) | |
3 | opelstrbas.v | . 2 β’ (π β π β π) | |
4 | opelstrbas.b | . 2 β’ (π β β¨(Baseβndx), πβ© β π) | |
5 | 1, 2, 3, 4 | opelstrsl 12576 | 1 β’ (π β π = (Baseβπ)) |
Colors of variables: wff set class |
Syntax hints: β wi 4 = wceq 1353 β wcel 2148 β¨cop 3597 class class class wbr 4005 βcfv 5218 Struct cstr 12461 ndxcnx 12462 Basecbs 12465 |
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-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4123 ax-pow 4176 ax-pr 4211 ax-un 4435 ax-cnex 7905 ax-resscn 7906 ax-1re 7908 ax-addrcl 7911 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2741 df-sbc 2965 df-dif 3133 df-un 3135 df-in 3137 df-ss 3144 df-nul 3425 df-pw 3579 df-sn 3600 df-pr 3601 df-op 3603 df-uni 3812 df-int 3847 df-br 4006 df-opab 4067 df-mpt 4068 df-id 4295 df-xp 4634 df-rel 4635 df-cnv 4636 df-co 4637 df-dm 4638 df-rn 4639 df-res 4640 df-iota 5180 df-fun 5220 df-fv 5226 df-inn 8923 df-struct 12467 df-ndx 12468 df-slot 12469 df-base 12471 |
This theorem is referenced by: 2strbas1g 12584 rngbaseg 12597 srngbased 12608 lmodbased 12626 ipsbased 12638 topgrpbasd 12658 |
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