Metamath Proof Explorer


Theorem 9t6e54

Description: 9 times 6 equals 54. (Contributed by Mario Carneiro, 19-Apr-2015)

Ref Expression
Assertion 9t6e54 ⊢ 9 ⋅ 6 = 54

Proof

Step Hyp Ref Expression
1 9nn0 ⊢ 9 ∈ ℕ 0
2 5nn0 ⊢ 5 ∈ ℕ 0
3 df-6 ⊢ 6 = 5 + 1
4 9t5e45 ⊢ 9 ⋅ 5 = 45
5 4nn0 ⊢ 4 ∈ ℕ 0
6 eqid ⊢ 45 = 45
7 4p1e5 ⊢ 4 + 1 = 5
8 1 nn0cni ⊢ 9 ∈ ℂ
9 2 nn0cni ⊢ 5 ∈ ℂ
10 9p5e14 ⊢ 9 + 5 = 14
11 8 9 10 addcomli ⊢ 5 + 9 = 14
12 5 2 1 6 7 5 11 decaddci ⊢ 45 + 9 = 54
13 1 2 3 4 12 4t3lem ⊢ 9 ⋅ 6 = 54