Metamath Proof Explorer


Theorem 3cn

Description: The number 3 is a complex number. (Contributed by FL, 17-Oct-2010) Reduce dependencies on axioms. (Revised by Steven Nguyen, 4-Oct-2022)

Ref Expression
Assertion 3cn ⊢ 3 ∈ ℂ

Proof

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