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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 15859 | . 2 ⊢ Struct = {〈𝑓, 𝑥〉 ∣ (𝑥 ∈ ( ≤ ∩ (ℕ × ℕ)) ∧ Fun (𝑓 ∖ {∅}) ∧ dom 𝑓 ⊆ (...‘𝑥))} | |
2 | 1 | relopabi 5245 | 1 ⊢ Rel Struct |
Colors of variables: wff setvar class |
Syntax hints: ∧ w3a 1037 ∈ wcel 1990 ∖ cdif 3571 ∩ cin 3573 ⊆ wss 3574 ∅c0 3915 {csn 4177 × cxp 5112 dom cdm 5114 Rel wrel 5119 Fun wfun 5882 ‘cfv 5888 ≤ cle 10075 ℕcn 11020 ...cfz 12326 Struct cstr 15853 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-opab 4713 df-xp 5120 df-rel 5121 df-struct 15859 |
This theorem is referenced by: isstruct2 15867 structex 15868 |
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