Description: 5 + 5 = 10. (Contributed by NM, 5-Feb-2007) (Revised by Stanislas Polu, 7-Apr-2020) (Revised by AV, 6-Sep-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | 5p5e10 | |- ( 5 + 5 ) = ; 1 0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-5 | |- 5 = ( 4 + 1 ) |
|
2 | 1 | oveq2i | |- ( 5 + 5 ) = ( 5 + ( 4 + 1 ) ) |
3 | 5cn | |- 5 e. CC |
|
4 | 4cn | |- 4 e. CC |
|
5 | ax-1cn | |- 1 e. CC |
|
6 | 3 4 5 | addassi | |- ( ( 5 + 4 ) + 1 ) = ( 5 + ( 4 + 1 ) ) |
7 | 2 6 | eqtr4i | |- ( 5 + 5 ) = ( ( 5 + 4 ) + 1 ) |
8 | 5p4e9 | |- ( 5 + 4 ) = 9 |
|
9 | 8 | oveq1i | |- ( ( 5 + 4 ) + 1 ) = ( 9 + 1 ) |
10 | 9p1e10 | |- ( 9 + 1 ) = ; 1 0 |
|
11 | 7 9 10 | 3eqtri | |- ( 5 + 5 ) = ; 1 0 |