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 )