Description: 5 + 2 = 7. (Contributed by NM, 11-May-2004)
Ref | Expression | ||
---|---|---|---|
Assertion | 5p2e7 | |- ( 5 + 2 ) = 7 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 | |- 2 = ( 1 + 1 ) |
|
2 | 1 | oveq2i | |- ( 5 + 2 ) = ( 5 + ( 1 + 1 ) ) |
3 | 5cn | |- 5 e. CC |
|
4 | ax-1cn | |- 1 e. CC |
|
5 | 3 4 4 | addassi | |- ( ( 5 + 1 ) + 1 ) = ( 5 + ( 1 + 1 ) ) |
6 | 2 5 | eqtr4i | |- ( 5 + 2 ) = ( ( 5 + 1 ) + 1 ) |
7 | df-6 | |- 6 = ( 5 + 1 ) |
|
8 | 7 | oveq1i | |- ( 6 + 1 ) = ( ( 5 + 1 ) + 1 ) |
9 | 6 8 | eqtr4i | |- ( 5 + 2 ) = ( 6 + 1 ) |
10 | df-7 | |- 7 = ( 6 + 1 ) |
|
11 | 9 10 | eqtr4i | |- ( 5 + 2 ) = 7 |