Description: Lemma for logcn . (Contributed by Mario Carneiro, 25-Feb-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | logcn.d | |
|
logcnlem.s | |
||
logcnlem.t | |
||
logcnlem.a | |
||
logcnlem.r | |
||
Assertion | logcnlem2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | logcn.d | |
|
2 | logcnlem.s | |
|
3 | logcnlem.t | |
|
4 | logcnlem.a | |
|
5 | logcnlem.r | |
|
6 | simpr | |
|
7 | 1 | ellogdm | |
8 | 7 | simplbi | |
9 | 4 8 | syl | |
10 | 9 | imcld | |
11 | 10 | adantr | |
12 | 11 | recnd | |
13 | reim0b | |
|
14 | 9 13 | syl | |
15 | 7 | simprbi | |
16 | 4 15 | syl | |
17 | 14 16 | sylbird | |
18 | 17 | necon3bd | |
19 | 18 | imp | |
20 | 12 19 | absrpcld | |
21 | 6 20 | ifclda | |
22 | 2 21 | eqeltrid | |
23 | 1 | logdmn0 | |
24 | 4 23 | syl | |
25 | 9 24 | absrpcld | |
26 | 1rp | |
|
27 | rpaddcl | |
|
28 | 26 5 27 | sylancr | |
29 | 5 28 | rpdivcld | |
30 | 25 29 | rpmulcld | |
31 | 3 30 | eqeltrid | |
32 | 22 31 | ifcld | |