Description: Lemma for lgamf . (Contributed by Mario Carneiro, 3-Jul-2017)
Ref | Expression | ||
---|---|---|---|
Hypotheses | dmgmn0.a | |
|
dmgmdivn0.a | |
||
Assertion | dmgmdivn0 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmgmn0.a | |
|
2 | dmgmdivn0.a | |
|
3 | 1 | eldifad | |
4 | 2 | nncnd | |
5 | 2 | nnne0d | |
6 | 3 4 4 5 | divdird | |
7 | 4 5 | dividd | |
8 | 7 | oveq2d | |
9 | 6 8 | eqtrd | |
10 | 3 4 | addcld | |
11 | 2 | nnnn0d | |
12 | dmgmaddn0 | |
|
13 | 1 11 12 | syl2anc | |
14 | 10 4 13 5 | divne0d | |
15 | 9 14 | eqnetrrd | |