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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 17190 | . 2 ⊢ Rel Struct | |
2 | 1 | brrelex1i 5755 | 1 ⊢ (𝐺 Struct 𝑋 → 𝐺 ∈ V) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2103 Vcvv 3482 class class class wbr 5169 Struct cstr 17188 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1793 ax-4 1807 ax-5 1909 ax-6 1967 ax-7 2007 ax-8 2105 ax-9 2113 ax-ext 2705 ax-sep 5320 ax-nul 5327 ax-pr 5450 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 847 df-3an 1089 df-tru 1540 df-fal 1550 df-ex 1778 df-sb 2065 df-clab 2712 df-cleq 2726 df-clel 2813 df-ral 3064 df-rex 3073 df-rab 3439 df-v 3484 df-dif 3973 df-un 3975 df-ss 3987 df-nul 4348 df-if 4549 df-sn 4649 df-pr 4651 df-op 4655 df-br 5170 df-opab 5232 df-xp 5705 df-rel 5706 df-struct 17189 |
This theorem is referenced by: setsn0fun 17215 setsstruct2 17216 strfv 17246 basprssdmsets 17266 opelstrbas 17267 cnfldexOLD 21400 edgfiedgval 29043 structgrssvtxlem 29049 setsiedg 29062 |
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