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Mirrors > Home > MPE Home > Th. List > brstruct | Structured version Visualization version GIF version |
Description: The structure relation is a relation. (Contributed by Mario Carneiro, 29-Aug-2015.) |
Ref | Expression |
---|---|
brstruct | ⊢ Rel Struct |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-struct 16776 | . 2 ⊢ Struct = {〈𝑓, 𝑥〉 ∣ (𝑥 ∈ ( ≤ ∩ (ℕ × ℕ)) ∧ Fun (𝑓 ∖ {∅}) ∧ dom 𝑓 ⊆ (...‘𝑥))} | |
2 | 1 | relopabiv 5719 | 1 ⊢ Rel Struct |
Colors of variables: wff setvar class |
Syntax hints: ∧ w3a 1085 ∈ wcel 2108 ∖ cdif 3880 ∩ cin 3882 ⊆ wss 3883 ∅c0 4253 {csn 4558 × cxp 5578 dom cdm 5580 Rel wrel 5585 Fun wfun 6412 ‘cfv 6418 ≤ cle 10941 ℕcn 11903 ...cfz 13168 Struct cstr 16775 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1799 ax-4 1813 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2110 ax-9 2118 ax-ext 2709 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1542 df-ex 1784 df-sb 2069 df-clab 2716 df-cleq 2730 df-clel 2817 df-v 3424 df-in 3890 df-ss 3900 df-opab 5133 df-xp 5586 df-rel 5587 df-struct 16776 |
This theorem is referenced by: isstruct2 16778 structex 16779 |
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