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 } ) ( 𝑓 ‘ 𝐴 ) = 0 ) )
2	1	simplbi	⊢ ( 𝐴 ∈ 𝔸 → 𝐴 ∈ ℂ )