Step |
Hyp |
Ref |
Expression |
1 |
|
msubco.s |
|
2 |
|
eqid |
|
3 |
|
eqid |
|
4 |
2 3 1
|
elmsubrn |
|
5 |
4
|
eleq2i |
|
6 |
|
eqid |
|
7 |
|
fvex |
|
8 |
7
|
mptex |
|
9 |
6 8
|
elrnmpti |
|
10 |
5 9
|
bitri |
|
11 |
2 3 1
|
elmsubrn |
|
12 |
11
|
eleq2i |
|
13 |
|
eqid |
|
14 |
7
|
mptex |
|
15 |
13 14
|
elrnmpti |
|
16 |
12 15
|
bitri |
|
17 |
|
reeanv |
|
18 |
|
simpr |
|
19 |
|
eqid |
|
20 |
|
eqid |
|
21 |
19 2 20
|
mexval |
|
22 |
18 21
|
eleqtrdi |
|
23 |
|
xp1st |
|
24 |
22 23
|
syl |
|
25 |
3 20
|
mrsubf |
|
26 |
25
|
ad2antlr |
|
27 |
|
xp2nd |
|
28 |
22 27
|
syl |
|
29 |
26 28
|
ffvelrnd |
|
30 |
|
opelxpi |
|
31 |
24 29 30
|
syl2anc |
|
32 |
31 21
|
eleqtrrdi |
|
33 |
|
eqidd |
|
34 |
|
eqidd |
|
35 |
|
fvex |
|
36 |
|
fvex |
|
37 |
35 36
|
op1std |
|
38 |
35 36
|
op2ndd |
|
39 |
38
|
fveq2d |
|
40 |
37 39
|
opeq12d |
|
41 |
32 33 34 40
|
fmptco |
|
42 |
|
fvco3 |
|
43 |
26 28 42
|
syl2anc |
|
44 |
43
|
opeq2d |
|
45 |
44
|
mpteq2dva |
|
46 |
41 45
|
eqtr4d |
|
47 |
3
|
mrsubco |
|
48 |
7
|
mptex |
|
49 |
|
eqid |
|
50 |
|
fveq1 |
|
51 |
50
|
opeq2d |
|
52 |
51
|
mpteq2dv |
|
53 |
49 52
|
elrnmpt1s |
|
54 |
47 48 53
|
sylancl |
|
55 |
2 3 1
|
elmsubrn |
|
56 |
54 55
|
eleqtrrdi |
|
57 |
46 56
|
eqeltrd |
|
58 |
|
coeq1 |
|
59 |
|
coeq2 |
|
60 |
58 59
|
sylan9eq |
|
61 |
60
|
eleq1d |
|
62 |
57 61
|
syl5ibrcom |
|
63 |
62
|
rexlimivv |
|
64 |
17 63
|
sylbir |
|
65 |
10 16 64
|
syl2anb |
|