Theorem cjcld

Description: Closure law for complex conjugate. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	recld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
Assertion	cjcld	⊢ ( 𝜑 → ( ∗ ‘ 𝐴 ) ∈ ℂ )

Proof

Step	Hyp	Ref	Expression
1		recld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		cjcl	⊢ ( 𝐴 ∈ ℂ → ( ∗ ‘ 𝐴 ) ∈ ℂ )
3	1 2	syl	⊢ ( 𝜑 → ( ∗ ‘ 𝐴 ) ∈ ℂ )