Metamath Proof Explorer


Theorem dp20h

Description: Add a zero in the unit places. (Contributed by Thierry Arnoux, 16-Dec-2021)

Ref Expression
Hypothesis dp20h.1 ⊢ A ∈ ℝ +
Assertion dp20h Could not format assertion : No typesetting found for |- _ 0 A = ( A / ; 1 0 ) with typecode |-

Proof

Step Hyp Ref Expression
1 dp20h.1 ⊢ A ∈ ℝ +
2 df-dp2 Could not format _ 0 A = ( 0 + ( A / ; 1 0 ) ) : No typesetting found for |- _ 0 A = ( 0 + ( A / ; 1 0 ) ) with typecode |-
3 rpcn ⊢ A ∈ ℝ + → A ∈ ℂ
4 1 3 ax-mp ⊢ A ∈ ℂ
5 10nn0 ⊢ 10 ∈ ℕ 0
6 5 nn0cni ⊢ 10 ∈ ℂ
7 0re ⊢ 0 ∈ ℝ
8 10pos ⊢ 0 < 10
9 7 8 gtneii ⊢ 10 ≠ 0
10 4 6 9 divcli ⊢ A 10 ∈ ℂ
11 10 addlidi ⊢ 0 + A 10 = A 10
12 2 11 eqtri Could not format _ 0 A = ( A / ; 1 0 ) : No typesetting found for |- _ 0 A = ( A / ; 1 0 ) with typecode |-