Description: 4 + 3 = 7. (Contributed by NM, 11-May-2004)
Ref | Expression | ||
---|---|---|---|
Assertion | 4p3e7 | |- ( 4 + 3 ) = 7 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3 | |- 3 = ( 2 + 1 ) |
|
2 | 1 | oveq2i | |- ( 4 + 3 ) = ( 4 + ( 2 + 1 ) ) |
3 | 4cn | |- 4 e. CC |
|
4 | 2cn | |- 2 e. CC |
|
5 | ax-1cn | |- 1 e. CC |
|
6 | 3 4 5 | addassi | |- ( ( 4 + 2 ) + 1 ) = ( 4 + ( 2 + 1 ) ) |
7 | 2 6 | eqtr4i | |- ( 4 + 3 ) = ( ( 4 + 2 ) + 1 ) |
8 | df-7 | |- 7 = ( 6 + 1 ) |
|
9 | 4p2e6 | |- ( 4 + 2 ) = 6 |
|
10 | 9 | oveq1i | |- ( ( 4 + 2 ) + 1 ) = ( 6 + 1 ) |
11 | 8 10 | eqtr4i | |- 7 = ( ( 4 + 2 ) + 1 ) |
12 | 7 11 | eqtr4i | |- ( 4 + 3 ) = 7 |