Step |
Hyp |
Ref |
Expression |
1 |
|
msubff.v |
|
2 |
|
msubff.r |
|
3 |
|
msubff.s |
|
4 |
|
eqid |
|
5 |
|
eqid |
|
6 |
1 2 3 4 5
|
msubffval |
|
7 |
6
|
rneqd |
|
8 |
1 2 5
|
mrsubff |
|
9 |
8
|
adantr |
|
10 |
9
|
ffund |
|
11 |
8
|
ffnd |
|
12 |
|
fnfvelrn |
|
13 |
11 12
|
sylan |
|
14 |
1 2 5
|
mrsubrn |
|
15 |
13 14
|
eleqtrdi |
|
16 |
|
fvelima |
|
17 |
10 15 16
|
syl2anc |
|
18 |
|
elmapi |
|
19 |
18
|
adantl |
|
20 |
|
ssid |
|
21 |
1 2 3 4 5
|
msubfval |
|
22 |
19 20 21
|
sylancl |
|
23 |
|
fvex |
|
24 |
23
|
mptex |
|
25 |
|
eqid |
|
26 |
24 25
|
fnmpti |
|
27 |
6
|
fneq1d |
|
28 |
26 27
|
mpbiri |
|
29 |
28
|
adantr |
|
30 |
|
mapsspm |
|
31 |
30
|
a1i |
|
32 |
|
simpr |
|
33 |
|
fnfvima |
|
34 |
29 31 32 33
|
syl3anc |
|
35 |
22 34
|
eqeltrrd |
|
36 |
35
|
adantlr |
|
37 |
|
fveq1 |
|
38 |
37
|
opeq2d |
|
39 |
38
|
mpteq2dv |
|
40 |
39
|
eleq1d |
|
41 |
36 40
|
syl5ibcom |
|
42 |
41
|
rexlimdva |
|
43 |
17 42
|
mpd |
|
44 |
43
|
fmpttd |
|
45 |
44
|
frnd |
|
46 |
7 45
|
eqsstrd |
|
47 |
3
|
rnfvprc |
|
48 |
|
0ss |
|
49 |
47 48
|
eqsstrdi |
|
50 |
46 49
|
pm2.61i |
|
51 |
|
imassrn |
|
52 |
50 51
|
eqssi |
|