Description: 9 times 3 equals 27. (Contributed by Mario Carneiro, 19-Apr-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | 9t3e27 | ⊢ ( 9 · 3 ) = ; 2 7 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 9nn0 | ⊢ 9 ∈ ℕ0 | |
2 | 2nn0 | ⊢ 2 ∈ ℕ0 | |
3 | df-3 | ⊢ 3 = ( 2 + 1 ) | |
4 | 9t2e18 | ⊢ ( 9 · 2 ) = ; 1 8 | |
5 | 1nn0 | ⊢ 1 ∈ ℕ0 | |
6 | 8nn0 | ⊢ 8 ∈ ℕ0 | |
7 | eqid | ⊢ ; 1 8 = ; 1 8 | |
8 | 1p1e2 | ⊢ ( 1 + 1 ) = 2 | |
9 | 7nn0 | ⊢ 7 ∈ ℕ0 | |
10 | 1 | nn0cni | ⊢ 9 ∈ ℂ |
11 | 6 | nn0cni | ⊢ 8 ∈ ℂ |
12 | 9p8e17 | ⊢ ( 9 + 8 ) = ; 1 7 | |
13 | 10 11 12 | addcomli | ⊢ ( 8 + 9 ) = ; 1 7 |
14 | 5 6 1 7 8 9 13 | decaddci | ⊢ ( ; 1 8 + 9 ) = ; 2 7 |
15 | 1 2 3 4 14 | 4t3lem | ⊢ ( 9 · 3 ) = ; 2 7 |