Description: 5 + 4 = 9. (Contributed by NM, 11-May-2004)
Ref | Expression | ||
---|---|---|---|
Assertion | 5p4e9 | |- ( 5 + 4 ) = 9 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-4 | |- 4 = ( 3 + 1 ) |
|
2 | 1 | oveq2i | |- ( 5 + 4 ) = ( 5 + ( 3 + 1 ) ) |
3 | 5cn | |- 5 e. CC |
|
4 | 3cn | |- 3 e. CC |
|
5 | ax-1cn | |- 1 e. CC |
|
6 | 3 4 5 | addassi | |- ( ( 5 + 3 ) + 1 ) = ( 5 + ( 3 + 1 ) ) |
7 | 2 6 | eqtr4i | |- ( 5 + 4 ) = ( ( 5 + 3 ) + 1 ) |
8 | df-9 | |- 9 = ( 8 + 1 ) |
|
9 | 5p3e8 | |- ( 5 + 3 ) = 8 |
|
10 | 9 | oveq1i | |- ( ( 5 + 3 ) + 1 ) = ( 8 + 1 ) |
11 | 8 10 | eqtr4i | |- 9 = ( ( 5 + 3 ) + 1 ) |
12 | 7 11 | eqtr4i | |- ( 5 + 4 ) = 9 |