Step |
Hyp |
Ref |
Expression |
1 |
|
tngval.t |
|
2 |
|
tngval.m |
|
3 |
|
tngval.d |
|
4 |
|
tngval.j |
|
5 |
|
elex |
|
6 |
|
elex |
|
7 |
|
simpl |
|
8 |
|
simpr |
|
9 |
7
|
fveq2d |
|
10 |
9 2
|
eqtr4di |
|
11 |
8 10
|
coeq12d |
|
12 |
11 3
|
eqtr4di |
|
13 |
12
|
opeq2d |
|
14 |
7 13
|
oveq12d |
|
15 |
12
|
fveq2d |
|
16 |
15 4
|
eqtr4di |
|
17 |
16
|
opeq2d |
|
18 |
14 17
|
oveq12d |
|
19 |
|
df-tng |
|
20 |
|
ovex |
|
21 |
18 19 20
|
ovmpoa |
|
22 |
5 6 21
|
syl2an |
|
23 |
1 22
|
syl5eq |
|