Description: 8 times 4 equals 32. (Contributed by Mario Carneiro, 19-Apr-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | 8t4e32 | |- ( 8 x. 4 ) = ; 3 2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 8nn0 | |- 8 e. NN0 |
|
2 | 3nn0 | |- 3 e. NN0 |
|
3 | df-4 | |- 4 = ( 3 + 1 ) |
|
4 | 8t3e24 | |- ( 8 x. 3 ) = ; 2 4 |
|
5 | 2nn0 | |- 2 e. NN0 |
|
6 | 4nn0 | |- 4 e. NN0 |
|
7 | eqid | |- ; 2 4 = ; 2 4 |
|
8 | 2p1e3 | |- ( 2 + 1 ) = 3 |
|
9 | 1 | nn0cni | |- 8 e. CC |
10 | 6 | nn0cni | |- 4 e. CC |
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 x. 4 ) = ; 3 2 |