Description: Sufficient conditions for ClWWalksNOn to be empty. (Contributed by AV, 25-Mar-2022)
Ref | Expression | ||
---|---|---|---|
Assertion | clwwlknon0 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq2 | |
|
2 | clwwlk0on0 | |
|
3 | 1 2 | eqtrdi | |
4 | 3 | a1d | |
5 | simprl | |
|
6 | elnnne0 | |
|
7 | 6 | simplbi2 | |
8 | 7 | adantl | |
9 | 8 | impcom | |
10 | 5 9 | jca | |
11 | 10 | stoic1a | |
12 | clwwlknonmpo | |
|
13 | 12 | mpondm0 | |
14 | 11 13 | syl | |
15 | 14 | ex | |
16 | 4 15 | pm2.61ine | |