Description: Value of the symbol concatenated with a word. (Contributed by Alexander van der Vekens, 5-Aug-2018) (Proof shortened by Alexander van der Vekens, 14-Oct-2018)
Ref | Expression | ||
---|---|---|---|
Assertion | ccats1val2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp1 | |
|
2 | s1cl | |
|
3 | 2 | 3ad2ant2 | |
4 | lencl | |
|
5 | 4 | nn0zd | |
6 | elfzomin | |
|
7 | 5 6 | syl | |
8 | s1len | |
|
9 | 8 | oveq2i | |
10 | 9 | oveq2i | |
11 | 7 10 | eleqtrrdi | |
12 | 11 | adantr | |
13 | eleq1 | |
|
14 | 13 | adantl | |
15 | 12 14 | mpbird | |
16 | 15 | 3adant2 | |
17 | ccatval2 | |
|
18 | 1 3 16 17 | syl3anc | |
19 | oveq1 | |
|
20 | 19 | 3ad2ant3 | |
21 | 4 | nn0cnd | |
22 | 21 | subidd | |
23 | 22 | 3ad2ant1 | |
24 | 20 23 | eqtrd | |
25 | 24 | fveq2d | |
26 | s1fv | |
|
27 | 26 | 3ad2ant2 | |
28 | 18 25 27 | 3eqtrd | |