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Mirrors > Home > ILE Home > Th. List > structex | GIF version |
Description: A structure is a set. (Contributed by AV, 10-Nov-2021.) |
Ref | Expression |
---|---|
structex | ⊢ (𝐺 Struct 𝑋 → 𝐺 ∈ V) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | brstruct 12601 | . 2 ⊢ Rel Struct | |
2 | 1 | brrelex1i 4694 | 1 ⊢ (𝐺 Struct 𝑋 → 𝐺 ∈ V) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 2160 Vcvv 2756 class class class wbr 4025 Struct cstr 12588 |
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-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4143 ax-pow 4199 ax-pr 4234 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2758 df-un 3153 df-in 3155 df-ss 3162 df-pw 3599 df-sn 3620 df-pr 3621 df-op 3623 df-br 4026 df-opab 4087 df-xp 4657 df-rel 4658 df-struct 12594 |
This theorem is referenced by: strsetsid 12625 setsn0fun 12629 strslfv 12637 strressid 12663 strleund 12695 strleun 12696 strext 12697 opelstrsl 12706 cnfldex 14014 |
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