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Mirrors > Home > ILE Home > Th. List > brstruct | 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 12000 | . 2 ⊢ Struct = {〈𝑓, 𝑥〉 ∣ (𝑥 ∈ ( ≤ ∩ (ℕ × ℕ)) ∧ Fun (𝑓 ∖ {∅}) ∧ dom 𝑓 ⊆ (...‘𝑥))} | |
2 | 1 | relopabi 4673 | 1 ⊢ Rel Struct |
Colors of variables: wff set class |
Syntax hints: ∧ w3a 963 ∈ wcel 1481 ∖ cdif 3073 ∩ cin 3075 ⊆ wss 3076 ∅c0 3368 {csn 3532 × cxp 4545 dom cdm 4547 Rel wrel 4552 Fun wfun 5125 ‘cfv 5131 ≤ cle 7825 ℕcn 8744 ...cfz 9821 Struct cstr 11994 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-opab 3998 df-xp 4553 df-rel 4554 df-struct 12000 |
This theorem is referenced by: isstruct2im 12008 structex 12010 |
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