Metamath Proof Explorer
Description: Closure of univariate polynomial degree in extended reals. (Contributed by Stefan O'Rear, 23-Mar-2015)
|
|
Ref |
Expression |
|
Hypotheses |
deg1xrf.d |
⊢ 𝐷 = ( deg1 ‘ 𝑅 ) |
|
|
deg1xrf.p |
⊢ 𝑃 = ( Poly1 ‘ 𝑅 ) |
|
|
deg1xrf.b |
⊢ 𝐵 = ( Base ‘ 𝑃 ) |
|
Assertion |
deg1xrcl |
⊢ ( 𝐹 ∈ 𝐵 → ( 𝐷 ‘ 𝐹 ) ∈ ℝ* ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
deg1xrf.d |
⊢ 𝐷 = ( deg1 ‘ 𝑅 ) |
2 |
|
deg1xrf.p |
⊢ 𝑃 = ( Poly1 ‘ 𝑅 ) |
3 |
|
deg1xrf.b |
⊢ 𝐵 = ( Base ‘ 𝑃 ) |
4 |
1 2 3
|
deg1xrf |
⊢ 𝐷 : 𝐵 ⟶ ℝ* |
5 |
4
|
ffvelrni |
⊢ ( 𝐹 ∈ 𝐵 → ( 𝐷 ‘ 𝐹 ) ∈ ℝ* ) |