Metamath Proof Explorer


Theorem 9cn

Description: The number 9 is a complex number. (Contributed by David A. Wheeler, 8-Dec-2018) Reduce dependencies on axioms. (Revised by Steven Nguyen, 4-Oct-2022)

Ref Expression
Assertion 9cn ⊢ 9 ∈ ℂ

Proof

Step Hyp Ref Expression
1 df-9 ⊢ 9 = 8 + 1
2 8cn ⊢ 8 ∈ ℂ
3 ax-1cn ⊢ 1 ∈ ℂ
4 2 3 addcli ⊢ 8 + 1 ∈ ℂ
5 1 4 eqeltri ⊢ 9 ∈ ℂ