Description: 8 times 4 equals 32. (Contributed by Mario Carneiro, 19-Apr-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | 8t4e32 | ⊢ ( 8 · 4 ) = ; 3 2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 8nn0 | ⊢ 8 ∈ ℕ0 | |
2 | 3nn0 | ⊢ 3 ∈ ℕ0 | |
3 | df-4 | ⊢ 4 = ( 3 + 1 ) | |
4 | 8t3e24 | ⊢ ( 8 · 3 ) = ; 2 4 | |
5 | 2nn0 | ⊢ 2 ∈ ℕ0 | |
6 | 4nn0 | ⊢ 4 ∈ ℕ0 | |
7 | eqid | ⊢ ; 2 4 = ; 2 4 | |
8 | 2p1e3 | ⊢ ( 2 + 1 ) = 3 | |
9 | 1 | nn0cni | ⊢ 8 ∈ ℂ |
10 | 6 | nn0cni | ⊢ 4 ∈ ℂ |
11 | 8p4e12 | ⊢ ( 8 + 4 ) = ; 1 2 | |
12 | 9 10 11 | addcomli | ⊢ ( 4 + 8 ) = ; 1 2 |
13 | 5 6 1 7 8 5 12 | decaddci | ⊢ ( ; 2 4 + 8 ) = ; 3 2 |
14 | 1 2 3 4 13 | 4t3lem | ⊢ ( 8 · 4 ) = ; 3 2 |