Theorem num0u

Description: Add a zero in the units place. (Contributed by Mario Carneiro, 18-Feb-2014)

	Ref	Expression
Hypotheses	numnncl.1	⊢ 𝑇 ∈ ℕ0
	numnncl.2	⊢ 𝐴 ∈ ℕ0
Assertion	num0u	⊢ ( 𝑇 · 𝐴 ) = ( ( 𝑇 · 𝐴 ) + 0 )

Proof

Step	Hyp	Ref	Expression
1		numnncl.1	⊢ 𝑇 ∈ ℕ0
2		numnncl.2	⊢ 𝐴 ∈ ℕ0
3	1 2	nn0mulcli	⊢ ( 𝑇 · 𝐴 ) ∈ ℕ0
4	3	nn0cni	⊢ ( 𝑇 · 𝐴 ) ∈ ℂ
5	4	addid1i	⊢ ( ( 𝑇 · 𝐴 ) + 0 ) = ( 𝑇 · 𝐴 )
6	5	eqcomi	⊢ ( 𝑇 · 𝐴 ) = ( ( 𝑇 · 𝐴 ) + 0 )