Description: Lemma 2 for walks to substitute the index of the condition for vertices and edges in a walk. (Contributed by AV, 23-Apr-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | wkslem2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq2 | |
|
2 | 1 | adantr | |
3 | fveq2 | |
|
4 | 3 | adantl | |
5 | 2 4 | eqeq12d | |
6 | 2fveq3 | |
|
7 | 1 | sneqd | |
8 | 6 7 | eqeq12d | |
9 | 8 | adantr | |
10 | 2 4 | preq12d | |
11 | 6 | adantr | |
12 | 10 11 | sseq12d | |
13 | 5 9 12 | ifpbi123d | |