Metamath Proof Explorer


Theorem 9t3e27

Description: 9 times 3 equals 27. (Contributed by Mario Carneiro, 19-Apr-2015)

Ref Expression
Assertion 9t3e27 ⊢ 9 ⋅ 3 = 27

Proof

Step Hyp Ref Expression
1 9nn0 ⊢ 9 ∈ ℕ 0
2 2nn0 ⊢ 2 ∈ ℕ 0
3 df-3 ⊢ 3 = 2 + 1
4 9t2e18 ⊢ 9 ⋅ 2 = 18
5 1nn0 ⊢ 1 ∈ ℕ 0
6 8nn0 ⊢ 8 ∈ ℕ 0
7 eqid ⊢ 18 = 18
8 1p1e2 ⊢ 1 + 1 = 2
9 7nn0 ⊢ 7 ∈ ℕ 0
10 1 nn0cni ⊢ 9 ∈ ℂ
11 6 nn0cni ⊢ 8 ∈ ℂ
12 9p8e17 ⊢ 9 + 8 = 17
13 10 11 12 addcomli ⊢ 8 + 9 = 17
14 5 6 1 7 8 9 13 decaddci ⊢ 18 + 9 = 27
15 1 2 3 4 14 4t3lem ⊢ 9 ⋅ 3 = 27