Metamath Proof Explorer


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