Step |
Hyp |
Ref |
Expression |
1 |
|
mendval.b |
|
2 |
|
mendval.p |
|
3 |
|
mendval.t |
|
4 |
|
mendval.s |
|
5 |
|
mendval.v |
|
6 |
|
elex |
|
7 |
|
oveq12 |
|
8 |
7
|
anidms |
|
9 |
8 1
|
eqtr4di |
|
10 |
9
|
csbeq1d |
|
11 |
|
ovex |
|
12 |
9 11
|
eqeltrrdi |
|
13 |
|
simpr |
|
14 |
13
|
opeq2d |
|
15 |
|
fveq2 |
|
16 |
|
ofeq |
|
17 |
15 16
|
syl |
|
18 |
17
|
oveqdr |
|
19 |
13 13 18
|
mpoeq123dv |
|
20 |
19 2
|
eqtr4di |
|
21 |
20
|
opeq2d |
|
22 |
|
eqidd |
|
23 |
13 13 22
|
mpoeq123dv |
|
24 |
23 3
|
eqtr4di |
|
25 |
24
|
opeq2d |
|
26 |
14 21 25
|
tpeq123d |
|
27 |
|
fveq2 |
|
28 |
27
|
adantr |
|
29 |
28 4
|
eqtr4di |
|
30 |
29
|
opeq2d |
|
31 |
29
|
fveq2d |
|
32 |
|
fveq2 |
|
33 |
32
|
adantr |
|
34 |
|
ofeq |
|
35 |
33 34
|
syl |
|
36 |
|
fveq2 |
|
37 |
36
|
adantr |
|
38 |
37
|
xpeq1d |
|
39 |
|
eqidd |
|
40 |
35 38 39
|
oveq123d |
|
41 |
31 13 40
|
mpoeq123dv |
|
42 |
41 5
|
eqtr4di |
|
43 |
42
|
opeq2d |
|
44 |
30 43
|
preq12d |
|
45 |
26 44
|
uneq12d |
|
46 |
12 45
|
csbied |
|
47 |
10 46
|
eqtrd |
|
48 |
|
df-mend |
|
49 |
|
tpex |
|
50 |
|
prex |
|
51 |
49 50
|
unex |
|
52 |
47 48 51
|
fvmpt |
|
53 |
6 52
|
syl |
|