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Mirrors > Home > MPE Home > Th. List > structex | Structured version Visualization version 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 15913 | . 2 ⊢ Rel Struct | |
2 | 1 | brrelexi 5192 | 1 ⊢ (𝐺 Struct 𝑋 → 𝐺 ∈ V) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2030 Vcvv 3231 class class class wbr 4685 Struct cstr 15900 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1762 ax-4 1777 ax-5 1879 ax-6 1945 ax-7 1981 ax-9 2039 ax-10 2059 ax-11 2074 ax-12 2087 ax-13 2282 ax-ext 2631 ax-sep 4814 ax-nul 4822 ax-pr 4936 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-3an 1056 df-tru 1526 df-ex 1745 df-nf 1750 df-sb 1938 df-clab 2638 df-cleq 2644 df-clel 2647 df-nfc 2782 df-ral 2946 df-rex 2947 df-rab 2950 df-v 3233 df-dif 3610 df-un 3612 df-in 3614 df-ss 3621 df-nul 3949 df-if 4120 df-sn 4211 df-pr 4213 df-op 4217 df-br 4686 df-opab 4746 df-xp 5149 df-rel 5150 df-struct 15906 |
This theorem is referenced by: setsn0fun 15942 setsstruct2 15943 strfv 15954 basprssdmsets 15972 opelstrbas 16025 cnfldex 19797 edgfiedgval 25947 structgrssvtxlem 25957 setsiedg 25973 |
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