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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 17196 | . 2 ⊢ Struct = {〈𝑓, 𝑥〉 ∣ (𝑥 ∈ ( ≤ ∩ (ℕ × ℕ)) ∧ Fun (𝑓 ∖ {∅}) ∧ dom 𝑓 ⊆ (...‘𝑥))} | |
2 | 1 | relopabiv 5844 | 1 ⊢ Rel Struct |
Colors of variables: wff setvar class |
Syntax hints: ∧ w3a 1087 ∈ wcel 2108 ∖ cdif 3973 ∩ cin 3975 ⊆ wss 3976 ∅c0 4352 {csn 4648 × cxp 5698 dom cdm 5700 Rel wrel 5705 Fun wfun 6569 ‘cfv 6575 ≤ cle 11327 ℕcn 12295 ...cfz 13569 Struct cstr 17195 |
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 2110 ax-9 2118 ax-ext 2711 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1540 df-ex 1778 df-sb 2065 df-clab 2718 df-cleq 2732 df-clel 2819 df-v 3490 df-ss 3993 df-opab 5229 df-xp 5706 df-rel 5707 df-struct 17196 |
This theorem is referenced by: isstruct2 17198 structex 17199 |
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