Description: Mapping of words commutes with the prefix operation. (Contributed by AV, 15-May-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | pfxco | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elfznn0 | |
|
2 | 1 | 3ad2ant2 | |
3 | 0elfz | |
|
4 | 2 3 | syl | |
5 | simp2 | |
|
6 | 4 5 | jca | |
7 | swrdco | |
|
8 | 6 7 | syld3an2 | |
9 | pfxval | |
|
10 | 1 9 | sylan2 | |
11 | 10 | coeq2d | |
12 | 11 | 3adant3 | |
13 | ffun | |
|
14 | 13 | anim2i | |
15 | 14 | ancomd | |
16 | 15 | 3adant2 | |
17 | cofunexg | |
|
18 | 16 17 | syl | |
19 | 18 2 | jca | |
20 | pfxval | |
|
21 | 19 20 | syl | |
22 | 8 12 21 | 3eqtr4d | |