Description: A univariate polynomial is a multivariate polynomial on one index. (Contributed by Stefan O'Rear, 25-Mar-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ply1bascl.p | ⊢ 𝑃 = ( Poly_{1} ‘ 𝑅 ) | |
ply1bascl.b | ⊢ 𝐵 = ( Base ‘ 𝑃 ) | ||
Assertion | ply1bascl2 | ⊢ ( 𝐹 ∈ 𝐵 → 𝐹 ∈ ( Base ‘ ( 1_{o} mPoly 𝑅 ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ply1bascl.p | ⊢ 𝑃 = ( Poly_{1} ‘ 𝑅 ) | |
2 | ply1bascl.b | ⊢ 𝐵 = ( Base ‘ 𝑃 ) | |
3 | eqid | ⊢ ( PwSer_{1} ‘ 𝑅 ) = ( PwSer_{1} ‘ 𝑅 ) | |
4 | 1 3 2 | ply1bas | ⊢ 𝐵 = ( Base ‘ ( 1_{o} mPoly 𝑅 ) ) |
5 | 4 | eleq2i | ⊢ ( 𝐹 ∈ 𝐵 ↔ 𝐹 ∈ ( Base ‘ ( 1_{o} mPoly 𝑅 ) ) ) |
6 | 5 | biimpi | ⊢ ( 𝐹 ∈ 𝐵 → 𝐹 ∈ ( Base ‘ ( 1_{o} mPoly 𝑅 ) ) ) |