Description: Value of a subword. (Contributed by Stefan O'Rear, 15-Aug-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | swrdval | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-substr | |
|
2 | 1 | a1i | |
3 | simprl | |
|
4 | fveq2 | |
|
5 | 4 | adantl | |
6 | op1stg | |
|
7 | 6 | 3adant1 | |
8 | 5 7 | sylan9eqr | |
9 | fveq2 | |
|
10 | 9 | adantl | |
11 | op2ndg | |
|
12 | 11 | 3adant1 | |
13 | 10 12 | sylan9eqr | |
14 | simp2 | |
|
15 | simp3 | |
|
16 | 14 15 | oveq12d | |
17 | simp1 | |
|
18 | 17 | dmeqd | |
19 | 16 18 | sseq12d | |
20 | 15 14 | oveq12d | |
21 | 20 | oveq2d | |
22 | 14 | oveq2d | |
23 | 17 22 | fveq12d | |
24 | 21 23 | mpteq12dv | |
25 | 19 24 | ifbieq1d | |
26 | 3 8 13 25 | syl3anc | |
27 | elex | |
|
28 | 27 | 3ad2ant1 | |
29 | opelxpi | |
|
30 | 29 | 3adant1 | |
31 | ovex | |
|
32 | 31 | mptex | |
33 | 0ex | |
|
34 | 32 33 | ifex | |
35 | 34 | a1i | |
36 | 2 26 28 30 35 | ovmpod | |