Metamath Proof Explorer


Theorem aacn

Description: An algebraic number is a complex number. (Contributed by Mario Carneiro, 23-Jul-2014)

Ref Expression
Assertion aacn ( 𝐴 ∈ 𝔸 → 𝐴 ∈ ℂ )

Proof

Step Hyp Ref Expression
1 elaa ( 𝐴 ∈ 𝔸 ↔ ( 𝐴 ∈ ℂ ∧ ∃ 𝑓 ∈ ( ( Poly ‘ ℤ ) ∖ { 0𝑝 } ) ( 𝑓𝐴 ) = 0 ) )
2 1 simplbi ( 𝐴 ∈ 𝔸 → 𝐴 ∈ ℂ )