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 ) = 4 0

Proof

Step Hyp Ref Expression
1 8nn0 ⊢ 8 ∈ ℕ0
2 4nn0 ⊢ 4 ∈ ℕ0
3 df-5 ⊢ 5 = ( 4 + 1 )
4 8t4e32 ⊢ ( 8 · 4 ) = 3 2
5 3nn0 ⊢ 3 ∈ ℕ0
6 2nn0 ⊢ 2 ∈ ℕ0
7 eqid ⊢ 3 2 = 3 2
8 3p1e4 ⊢ ( 3 + 1 ) = 4
9 8cn ⊢ 8 ∈ ℂ
10 2cn ⊢ 2 ∈ ℂ
11 8p2e10 ⊢ ( 8 + 2 ) = 1 0
12 9 10 11 addcomli ⊢ ( 2 + 8 ) = 1 0
13 5 6 1 7 8 12 decaddci2 ⊢ ( 3 2 + 8 ) = 4 0
14 1 2 3 4 13 4t3lem ⊢ ( 8 · 5 ) = 4 0