Description: Domain and codomain of the arcsin function. (Contributed by Mario Carneiro, 31-Mar-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | asinf | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-asin | |
|
2 | negicn | |
|
3 | ax-icn | |
|
4 | mulcl | |
|
5 | 3 4 | mpan | |
6 | ax-1cn | |
|
7 | sqcl | |
|
8 | subcl | |
|
9 | 6 7 8 | sylancr | |
10 | 9 | sqrtcld | |
11 | 5 10 | addcld | |
12 | asinlem | |
|
13 | 11 12 | logcld | |
14 | mulcl | |
|
15 | 2 13 14 | sylancr | |
16 | 1 15 | fmpti | |