Theorem cjcli

Description: Closure law for complex conjugate. (Contributed by NM, 11-May-1999)

	Ref	Expression
Hypothesis	recl.1	⊢ 𝐴 ∈ ℂ
Assertion	cjcli	⊢ ( ∗ ‘ 𝐴 ) ∈ ℂ

Proof

Step	Hyp	Ref	Expression
1		recl.1	⊢ 𝐴 ∈ ℂ
2		cjcl	⊢ ( 𝐴 ∈ ℂ → ( ∗ ‘ 𝐴 ) ∈ ℂ )
3	1 2	ax-mp	⊢ ( ∗ ‘ 𝐴 ) ∈ ℂ