Description: 7 + 3 = 10. (Contributed by NM, 5-Feb-2007) (Revised by Stanislas Polu, 7-Apr-2020) (Revised by AV, 6-Sep-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | 7p3e10 | |- ( 7 + 3 ) = ; 1 0 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-3 | |- 3 = ( 2 + 1 ) |
|
| 2 | 1 | oveq2i | |- ( 7 + 3 ) = ( 7 + ( 2 + 1 ) ) |
| 3 | 7cn | |- 7 e. CC |
|
| 4 | 2cn | |- 2 e. CC |
|
| 5 | ax-1cn | |- 1 e. CC |
|
| 6 | 3 4 5 | addassi | |- ( ( 7 + 2 ) + 1 ) = ( 7 + ( 2 + 1 ) ) |
| 7 | 2 6 | eqtr4i | |- ( 7 + 3 ) = ( ( 7 + 2 ) + 1 ) |
| 8 | 7p2e9 | |- ( 7 + 2 ) = 9 |
|
| 9 | 8 | oveq1i | |- ( ( 7 + 2 ) + 1 ) = ( 9 + 1 ) |
| 10 | 9p1e10 | |- ( 9 + 1 ) = ; 1 0 |
|
| 11 | 7 9 10 | 3eqtri | |- ( 7 + 3 ) = ; 1 0 |