![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 17150 | . 2 ⊢ Rel Struct | |
2 | 1 | brrelex1i 5738 | 1 ⊢ (𝐺 Struct 𝑋 → 𝐺 ∈ V) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2099 Vcvv 3462 class class class wbr 5153 Struct cstr 17148 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2697 ax-sep 5304 ax-nul 5311 ax-pr 5433 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3an 1086 df-tru 1537 df-fal 1547 df-ex 1775 df-sb 2061 df-clab 2704 df-cleq 2718 df-clel 2803 df-ral 3052 df-rex 3061 df-rab 3420 df-v 3464 df-dif 3950 df-un 3952 df-ss 3964 df-nul 4326 df-if 4534 df-sn 4634 df-pr 4636 df-op 4640 df-br 5154 df-opab 5216 df-xp 5688 df-rel 5689 df-struct 17149 |
This theorem is referenced by: setsn0fun 17175 setsstruct2 17176 strfv 17206 basprssdmsets 17226 opelstrbas 17227 cnfldexOLD 21361 edgfiedgval 28953 structgrssvtxlem 28959 setsiedg 28972 |
Copyright terms: Public domain | W3C validator |