Description: 11 is 1 times 10 to the power of 1, plus 1. (Contributed by AV, 4-Aug-2020) (Revised by AV, 9-Sep-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | 1t10e1p1e11 | |- ; 1 1 = ( ( 1 x. ( ; 1 0 ^ 1 ) ) + 1 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfdec10 | |- ; 1 1 = ( ( ; 1 0 x. 1 ) + 1 ) |
|
2 | ax-1cn | |- 1 e. CC |
|
3 | 10nn | |- ; 1 0 e. NN |
|
4 | 3 | nncni | |- ; 1 0 e. CC |
5 | exp1 | |- ( ; 1 0 e. CC -> ( ; 1 0 ^ 1 ) = ; 1 0 ) |
|
6 | 4 5 | ax-mp | |- ( ; 1 0 ^ 1 ) = ; 1 0 |
7 | 6 | eqcomi | |- ; 1 0 = ( ; 1 0 ^ 1 ) |
8 | 7 | oveq2i | |- ( 1 x. ; 1 0 ) = ( 1 x. ( ; 1 0 ^ 1 ) ) |
9 | 2 4 8 | mulcomli | |- ( ; 1 0 x. 1 ) = ( 1 x. ( ; 1 0 ^ 1 ) ) |
10 | 9 | oveq1i | |- ( ( ; 1 0 x. 1 ) + 1 ) = ( ( 1 x. ( ; 1 0 ^ 1 ) ) + 1 ) |
11 | 1 10 | eqtri | |- ; 1 1 = ( ( 1 x. ( ; 1 0 ^ 1 ) ) + 1 ) |