Metamath Proof Explorer


Theorem deg1xrcl

Description: Closure of univariate polynomial degree in extended reals. (Contributed by Stefan O'Rear, 23-Mar-2015)

Ref Expression
Hypotheses deg1xrf.d 𝐷 = ( deg1𝑅 )
deg1xrf.p 𝑃 = ( Poly1𝑅 )
deg1xrf.b 𝐵 = ( Base ‘ 𝑃 )
Assertion deg1xrcl ( 𝐹𝐵 → ( 𝐷𝐹 ) ∈ ℝ* )

Proof

Step Hyp Ref Expression
1 deg1xrf.d 𝐷 = ( deg1𝑅 )
2 deg1xrf.p 𝑃 = ( Poly1𝑅 )
3 deg1xrf.b 𝐵 = ( Base ‘ 𝑃 )
4 1 2 3 deg1xrf 𝐷 : 𝐵 ⟶ ℝ*
5 4 ffvelrni ( 𝐹𝐵 → ( 𝐷𝐹 ) ∈ ℝ* )