Description: 8 times 5 equals 40. (Contributed by Mario Carneiro, 19-Apr-2015) (Revised by AV, 6-Sep-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | 8t5e40 | |- ( 8 x. 5 ) = ; 4 0 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 8nn0 | |- 8 e. NN0 |
|
| 2 | 4nn0 | |- 4 e. NN0 |
|
| 3 | df-5 | |- 5 = ( 4 + 1 ) |
|
| 4 | 8t4e32 | |- ( 8 x. 4 ) = ; 3 2 |
|
| 5 | 3nn0 | |- 3 e. NN0 |
|
| 6 | 2nn0 | |- 2 e. NN0 |
|
| 7 | eqid | |- ; 3 2 = ; 3 2 |
|
| 8 | 3p1e4 | |- ( 3 + 1 ) = 4 |
|
| 9 | 8cn | |- 8 e. CC |
|
| 10 | 2cn | |- 2 e. CC |
|
| 11 | 8p2e10 | |- ( 8 + 2 ) = ; 1 0 |
|
| 12 | 9 10 11 | addcomli | |- ( 2 + 8 ) = ; 1 0 |
| 13 | 5 6 1 7 8 12 | decaddci2 | |- ( ; 3 2 + 8 ) = ; 4 0 |
| 14 | 1 2 3 4 13 | 4t3lem | |- ( 8 x. 5 ) = ; 4 0 |