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Metamath Proof Explorer
Description: The category of extensible structures is a category. (Contributed by AV, 8-Mar-2020)
|
|
Ref |
Expression |
|
Hypothesis |
estrccat.c |
⊢ 𝐶 = ( ExtStrCat ‘ 𝑈 ) |
|
Assertion |
estrccat |
⊢ ( 𝑈 ∈ 𝑉 → 𝐶 ∈ Cat ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
estrccat.c |
⊢ 𝐶 = ( ExtStrCat ‘ 𝑈 ) |
| 2 |
1
|
estrccatid |
⊢ ( 𝑈 ∈ 𝑉 → ( 𝐶 ∈ Cat ∧ ( Id ‘ 𝐶 ) = ( 𝑥 ∈ 𝑈 ↦ ( I ↾ ( Base ‘ 𝑥 ) ) ) ) ) |
| 3 |
2
|
simpld |
⊢ ( 𝑈 ∈ 𝑉 → 𝐶 ∈ Cat ) |