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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 12340 | . 2 ⊢ Rel Struct | |
2 | 1 | brrelex1i 4641 | 1 ⊢ (𝐺 Struct 𝑋 → 𝐺 ∈ V) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 2135 Vcvv 2721 class class class wbr 3976 Struct cstr 12327 |
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-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-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-br 3977 df-opab 4038 df-xp 4604 df-rel 4605 df-struct 12333 |
This theorem is referenced by: strsetsid 12364 setsn0fun 12368 strslfv 12375 strleund 12419 strleun 12420 opelstrsl 12427 |
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