Metamath Proof Explorer


Theorem addcomnni

Description: Commutative law for addition. (Contributed by metakunt, 25-Apr-2024)

Ref Expression
Hypotheses addcomnni.1 ⊢ A ∈ ℕ
addcomnni.2 ⊢ B ∈ ℕ
Assertion addcomnni ⊢ A + B = B + A

Proof

Step Hyp Ref Expression
1 addcomnni.1 ⊢ A ∈ ℕ
2 addcomnni.2 ⊢ B ∈ ℕ
3 1 nncni ⊢ A ∈ ℂ
4 2 nncni ⊢ B ∈ ℂ
5 3 4 addcomi ⊢ A + B = B + A