Step |
Hyp |
Ref |
Expression |
1 |
|
mrsubffval.c |
|
2 |
|
mrsubffval.v |
|
3 |
|
mrsubffval.r |
|
4 |
|
mrsubffval.s |
|
5 |
|
simp3 |
|
6 |
5
|
s1cld |
|
7 |
|
elun |
|
8 |
|
elfvex |
|
9 |
8 1
|
eleq2s |
|
10 |
|
elfvex |
|
11 |
10 2
|
eleq2s |
|
12 |
9 11
|
jaoi |
|
13 |
7 12
|
sylbi |
|
14 |
13
|
3ad2ant3 |
|
15 |
1 2 3
|
mrexval |
|
16 |
14 15
|
syl |
|
17 |
6 16
|
eleqtrrd |
|
18 |
|
eqid |
|
19 |
1 2 3 4 18
|
mrsubval |
|
20 |
17 19
|
syld3an3 |
|
21 |
|
simpl1 |
|
22 |
21
|
ffvelrnda |
|
23 |
16
|
ad2antrr |
|
24 |
22 23
|
eleqtrd |
|
25 |
|
simplr |
|
26 |
25
|
s1cld |
|
27 |
24 26
|
ifclda |
|
28 |
27
|
fmpttd |
|
29 |
|
s1co |
|
30 |
5 28 29
|
syl2anc |
|
31 |
|
eleq1 |
|
32 |
|
fveq2 |
|
33 |
|
s1eq |
|
34 |
31 32 33
|
ifbieq12d |
|
35 |
|
eqid |
|
36 |
|
fvex |
|
37 |
|
s1cli |
|
38 |
37
|
elexi |
|
39 |
36 38
|
ifex |
|
40 |
34 35 39
|
fvmpt |
|
41 |
40
|
3ad2ant3 |
|
42 |
41
|
s1eqd |
|
43 |
30 42
|
eqtrd |
|
44 |
43
|
oveq2d |
|
45 |
28 5
|
ffvelrnd |
|
46 |
41 45
|
eqeltrrd |
|
47 |
1
|
fvexi |
|
48 |
2
|
fvexi |
|
49 |
47 48
|
unex |
|
50 |
|
eqid |
|
51 |
18 50
|
frmdbas |
|
52 |
49 51
|
ax-mp |
|
53 |
52
|
eqcomi |
|
54 |
53
|
gsumws1 |
|
55 |
46 54
|
syl |
|
56 |
20 44 55
|
3eqtrd |
|