Theorem cjcl

Description: The conjugate of a complex number is a complex number (closure law). (Contributed by NM, 10-May-1999) (Revised by Mario Carneiro, 6-Nov-2013)

	Ref	Expression
Assertion	cjcl	⊢ ( 𝐴 ∈ ℂ → ( ∗ ‘ 𝐴 ) ∈ ℂ )

Proof

Step	Hyp	Ref	Expression
1		cjf	⊢ ∗ : ℂ ⟶ ℂ
2	1	ffvelcdmi	⊢ ( 𝐴 ∈ ℂ → ( ∗ ‘ 𝐴 ) ∈ ℂ )