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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 ∈ ℕ 0
numnncl.2 ⊢ A ∈ ℕ 0
Assertion num0u ⊢ T ⁢ A = T ⁢ A + 0

Proof

Step Hyp Ref Expression
1 numnncl.1 ⊢ T ∈ ℕ 0
2 numnncl.2 ⊢ A ∈ ℕ 0
3 1 2 nn0mulcli ⊢ T ⁢ A ∈ ℕ 0
4 3 nn0cni ⊢ T ⁢ A ∈ ℂ
5 4 addridi ⊢ T ⁢ A + 0 = T ⁢ A
6 5 eqcomi ⊢ T ⁢ A = T ⁢ A + 0