Metamath Proof Explorer


Theorem 8t5e40

Description: 8 times 5 equals 40. (Contributed by Mario Carneiro, 19-Apr-2015) (Revised by AV, 6-Sep-2021)

Ref Expression
Assertion 8t5e40 ⊢ 8 ⋅ 5 = 40

Proof

Step Hyp Ref Expression
1 8nn0 ⊢ 8 ∈ ℕ 0
2 4nn0 ⊢ 4 ∈ ℕ 0
3 df-5 ⊢ 5 = 4 + 1
4 8t4e32 ⊢ 8 ⋅ 4 = 32
5 3nn0 ⊢ 3 ∈ ℕ 0
6 2nn0 ⊢ 2 ∈ ℕ 0
7 eqid ⊢ 32 = 32
8 3p1e4 ⊢ 3 + 1 = 4
9 8cn ⊢ 8 ∈ ℂ
10 2cn ⊢ 2 ∈ ℂ
11 8p2e10 ⊢ 8 + 2 = 10
12 9 10 11 addcomli ⊢ 2 + 8 = 10
13 5 6 1 7 8 12 decaddci2 ⊢ 32 + 8 = 40
14 1 2 3 4 13 4t3lem ⊢ 8 ⋅ 5 = 40