Description: The logarithm of 1 to an arbitrary base B is 0. Property 1(b) of Cohen4 p. 361. See log1 . (Contributed by Stefan O'Rear, 19-Sep-2014) (Revised by Thierry Arnoux, 27-Sep-2017)
Ref | Expression | ||
---|---|---|---|
Assertion | logb1 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldifpr | |
|
2 | ax-1cn | |
|
3 | ax-1ne0 | |
|
4 | eldifsn | |
|
5 | 2 3 4 | mpbir2an | |
6 | logbval | |
|
7 | 5 6 | mpan2 | |
8 | 1 7 | sylbir | |
9 | log1 | |
|
10 | 9 | oveq1i | |
11 | simp1 | |
|
12 | simp2 | |
|
13 | 11 12 | logcld | |
14 | logccne0 | |
|
15 | 13 14 | div0d | |
16 | 10 15 | eqtrid | |
17 | 8 16 | eqtrd | |