Metamath Proof Explorer
Description: The sum of two multiples of 10 is a multiple of 10. (Contributed by AV, 30-Jul-2021)
|
|
Ref |
Expression |
|
Hypotheses |
decaddm10.a |
⊢ 𝐴 ∈ ℕ0 |
|
|
decaddm10.b |
⊢ 𝐵 ∈ ℕ0 |
|
Assertion |
decaddm10 |
⊢ ( ; 𝐴 0 + ; 𝐵 0 ) = ; ( 𝐴 + 𝐵 ) 0 |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
decaddm10.a |
⊢ 𝐴 ∈ ℕ0 |
2 |
|
decaddm10.b |
⊢ 𝐵 ∈ ℕ0 |
3 |
|
0nn0 |
⊢ 0 ∈ ℕ0 |
4 |
|
eqid |
⊢ ; 𝐴 0 = ; 𝐴 0 |
5 |
|
eqid |
⊢ ; 𝐵 0 = ; 𝐵 0 |
6 |
|
eqid |
⊢ ( 𝐴 + 𝐵 ) = ( 𝐴 + 𝐵 ) |
7 |
|
00id |
⊢ ( 0 + 0 ) = 0 |
8 |
1 3 2 3 4 5 6 7
|
decadd |
⊢ ( ; 𝐴 0 + ; 𝐵 0 ) = ; ( 𝐴 + 𝐵 ) 0 |