Step |
Hyp |
Ref |
Expression |
1 |
|
s3rn.i |
|
2 |
|
s3rn.j |
|
3 |
|
s3rn.k |
|
4 |
|
imadmrn |
|
5 |
1 2 3
|
s3cld |
|
6 |
|
wrdfn |
|
7 |
|
s3len |
|
8 |
7
|
oveq2i |
|
9 |
|
fzo0to3tp |
|
10 |
8 9
|
eqtri |
|
11 |
10
|
fneq2i |
|
12 |
11
|
biimpi |
|
13 |
5 6 12
|
3syl |
|
14 |
13
|
fndmd |
|
15 |
14
|
imaeq2d |
|
16 |
|
c0ex |
|
17 |
16
|
tpid1 |
|
18 |
17
|
a1i |
|
19 |
|
1ex |
|
20 |
19
|
tpid2 |
|
21 |
20
|
a1i |
|
22 |
|
2ex |
|
23 |
22
|
tpid3 |
|
24 |
23
|
a1i |
|
25 |
13 18 21 24
|
fnimatp |
|
26 |
|
s3fv0 |
|
27 |
1 26
|
syl |
|
28 |
|
s3fv1 |
|
29 |
2 28
|
syl |
|
30 |
|
s3fv2 |
|
31 |
3 30
|
syl |
|
32 |
27 29 31
|
tpeq123d |
|
33 |
15 25 32
|
3eqtrd |
|
34 |
4 33
|
syl5eqr |
|