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Metamath Proof Explorer
Description: Graph isomorphism is reflexive for hypergraphs. (Contributed by AV, 11-Nov-2022) (Revised by AV, 29-Apr-2025)
|
|
Ref |
Expression |
|
Assertion |
gricref |
⊢ ( 𝐺 ∈ UHGraph → 𝐺 ≃𝑔𝑟 𝐺 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
grimid |
⊢ ( 𝐺 ∈ UHGraph → ( I ↾ ( Vtx ‘ 𝐺 ) ) ∈ ( 𝐺 GraphIso 𝐺 ) ) |
| 2 |
|
brgrici |
⊢ ( ( I ↾ ( Vtx ‘ 𝐺 ) ) ∈ ( 𝐺 GraphIso 𝐺 ) → 𝐺 ≃𝑔𝑟 𝐺 ) |
| 3 |
1 2
|
syl |
⊢ ( 𝐺 ∈ UHGraph → 𝐺 ≃𝑔𝑟 𝐺 ) |