Step |
Hyp |
Ref |
Expression |
1 |
|
msubvrs.s |
|
2 |
|
msubvrs.e |
|
3 |
|
msubvrs.v |
|
4 |
|
msubvrs.h |
|
5 |
|
eqid |
|
6 |
2 5 1
|
elmsubrn |
|
7 |
6
|
eleq2i |
|
8 |
|
eqid |
|
9 |
2
|
fvexi |
|
10 |
9
|
mptex |
|
11 |
8 10
|
elrnmpti |
|
12 |
7 11
|
bitri |
|
13 |
|
simp2 |
|
14 |
|
simp3 |
|
15 |
|
eqid |
|
16 |
|
eqid |
|
17 |
15 2 16
|
mexval |
|
18 |
14 17
|
eleqtrdi |
|
19 |
|
xp2nd |
|
20 |
18 19
|
syl |
|
21 |
|
eqid |
|
22 |
5 21 16
|
mrsubvrs |
|
23 |
13 20 22
|
syl2anc |
|
24 |
|
fveq2 |
|
25 |
|
2fveq3 |
|
26 |
24 25
|
opeq12d |
|
27 |
|
eqid |
|
28 |
|
opex |
|
29 |
26 27 28
|
fvmpt3i |
|
30 |
14 29
|
syl |
|
31 |
30
|
fveq2d |
|
32 |
|
xp1st |
|
33 |
18 32
|
syl |
|
34 |
5 16
|
mrsubf |
|
35 |
13 34
|
syl |
|
36 |
19 17
|
eleq2s |
|
37 |
14 36
|
syl |
|
38 |
35 37
|
ffvelrnd |
|
39 |
|
opelxpi |
|
40 |
33 38 39
|
syl2anc |
|
41 |
40 17
|
eleqtrrdi |
|
42 |
21 2 3
|
mvrsval |
|
43 |
41 42
|
syl |
|
44 |
|
fvex |
|
45 |
|
fvex |
|
46 |
44 45
|
op2nd |
|
47 |
46
|
a1i |
|
48 |
47
|
rneqd |
|
49 |
48
|
ineq1d |
|
50 |
31 43 49
|
3eqtrd |
|
51 |
21 2 3
|
mvrsval |
|
52 |
14 51
|
syl |
|
53 |
52
|
iuneq1d |
|
54 |
21 2 4
|
mvhf |
|
55 |
54
|
3ad2ant1 |
|
56 |
|
inss2 |
|
57 |
56
|
sseli |
|
58 |
|
ffvelrn |
|
59 |
55 57 58
|
syl2an |
|
60 |
|
fveq2 |
|
61 |
|
2fveq3 |
|
62 |
60 61
|
opeq12d |
|
63 |
62 27 28
|
fvmpt3i |
|
64 |
59 63
|
syl |
|
65 |
57
|
adantl |
|
66 |
|
eqid |
|
67 |
21 66 4
|
mvhval |
|
68 |
65 67
|
syl |
|
69 |
|
fvex |
|
70 |
|
s1cli |
|
71 |
70
|
elexi |
|
72 |
69 71
|
op1std |
|
73 |
68 72
|
syl |
|
74 |
69 71
|
op2ndd |
|
75 |
68 74
|
syl |
|
76 |
75
|
fveq2d |
|
77 |
73 76
|
opeq12d |
|
78 |
64 77
|
eqtrd |
|
79 |
78
|
fveq2d |
|
80 |
|
simpl1 |
|
81 |
21 15 66
|
mtyf2 |
|
82 |
80 81
|
syl |
|
83 |
82 65
|
ffvelrnd |
|
84 |
35
|
adantr |
|
85 |
|
elun2 |
|
86 |
65 85
|
syl |
|
87 |
86
|
s1cld |
|
88 |
|
eqid |
|
89 |
88 21 16
|
mrexval |
|
90 |
80 89
|
syl |
|
91 |
87 90
|
eleqtrrd |
|
92 |
84 91
|
ffvelrnd |
|
93 |
|
opelxpi |
|
94 |
83 92 93
|
syl2anc |
|
95 |
94 17
|
eleqtrrdi |
|
96 |
21 2 3
|
mvrsval |
|
97 |
95 96
|
syl |
|
98 |
|
fvex |
|
99 |
69 98
|
op2nd |
|
100 |
99
|
a1i |
|
101 |
100
|
rneqd |
|
102 |
101
|
ineq1d |
|
103 |
79 97 102
|
3eqtrd |
|
104 |
103
|
iuneq2dv |
|
105 |
53 104
|
eqtrd |
|
106 |
23 50 105
|
3eqtr4d |
|
107 |
|
fveq1 |
|
108 |
107
|
fveq2d |
|
109 |
|
fveq1 |
|
110 |
109
|
fveq2d |
|
111 |
110
|
iuneq2d |
|
112 |
108 111
|
eqeq12d |
|
113 |
106 112
|
syl5ibrcom |
|
114 |
113
|
3expia |
|
115 |
114
|
com23 |
|
116 |
115
|
rexlimdva |
|
117 |
12 116
|
syl5bi |
|
118 |
117
|
3imp |
|