This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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 addridi ⊢ ( ( 𝑇 · 𝐴 ) + 0 ) = ( 𝑇 · 𝐴 )
6 5 eqcomi ⊢ ( 𝑇 · 𝐴 ) = ( ( 𝑇 · 𝐴 ) + 0 )