Step |
Hyp |
Ref |
Expression |
1 |
|
hsmexlem4.x |
|
2 |
|
hsmexlem4.h |
|
3 |
|
hsmexlem4.u |
|
4 |
|
hsmexlem4.s |
|
5 |
|
hsmexlem4.o |
|
6 |
|
fveq2 |
|
7 |
6
|
imaeq2d |
|
8 |
|
oieq2 |
|
9 |
7 8
|
syl |
|
10 |
5 9
|
syl5eq |
|
11 |
10
|
dmeqd |
|
12 |
|
fveq2 |
|
13 |
11 12
|
eleq12d |
|
14 |
13
|
ralbidv |
|
15 |
|
fveq2 |
|
16 |
15
|
imaeq2d |
|
17 |
|
oieq2 |
|
18 |
16 17
|
syl |
|
19 |
5 18
|
syl5eq |
|
20 |
19
|
dmeqd |
|
21 |
|
fveq2 |
|
22 |
20 21
|
eleq12d |
|
23 |
22
|
ralbidv |
|
24 |
|
fveq2 |
|
25 |
24
|
imaeq2d |
|
26 |
|
oieq2 |
|
27 |
25 26
|
syl |
|
28 |
5 27
|
syl5eq |
|
29 |
28
|
dmeqd |
|
30 |
|
fveq2 |
|
31 |
29 30
|
eleq12d |
|
32 |
31
|
ralbidv |
|
33 |
|
imassrn |
|
34 |
|
rankf |
|
35 |
|
frn |
|
36 |
34 35
|
ax-mp |
|
37 |
33 36
|
sstri |
|
38 |
3
|
ituni0 |
|
39 |
38
|
elv |
|
40 |
39
|
imaeq2i |
|
41 |
|
ffun |
|
42 |
34 41
|
ax-mp |
|
43 |
|
vex |
|
44 |
|
wdomimag |
|
45 |
42 43 44
|
mp2an |
|
46 |
|
sneq |
|
47 |
46
|
fveq2d |
|
48 |
47
|
raleqdv |
|
49 |
48 4
|
elrab2 |
|
50 |
49
|
simprbi |
|
51 |
|
snex |
|
52 |
|
tcid |
|
53 |
51 52
|
ax-mp |
|
54 |
|
vsnid |
|
55 |
53 54
|
sselii |
|
56 |
|
breq1 |
|
57 |
56
|
rspcv |
|
58 |
55 57
|
ax-mp |
|
59 |
|
domwdom |
|
60 |
50 58 59
|
3syl |
|
61 |
|
wdomtr |
|
62 |
45 60 61
|
sylancr |
|
63 |
40 62
|
eqbrtrid |
|
64 |
|
eqid |
|
65 |
64
|
hsmexlem1 |
|
66 |
37 63 65
|
sylancr |
|
67 |
2
|
hsmexlem7 |
|
68 |
66 67
|
eleqtrrdi |
|
69 |
68
|
rgen |
|
70 |
|
nfra1 |
|
71 |
|
nfv |
|
72 |
70 71
|
nfan |
|
73 |
3
|
ituniiun |
|
74 |
73
|
elv |
|
75 |
74
|
imaeq2i |
|
76 |
|
imaiun |
|
77 |
75 76
|
eqtri |
|
78 |
|
oieq2 |
|
79 |
77 78
|
ax-mp |
|
80 |
79
|
dmeqi |
|
81 |
60
|
ad2antll |
|
82 |
2
|
hsmexlem9 |
|
83 |
82
|
ad2antrl |
|
84 |
|
fveq2 |
|
85 |
84
|
fveq1d |
|
86 |
85
|
imaeq2d |
|
87 |
|
oieq2 |
|
88 |
86 87
|
syl |
|
89 |
88
|
dmeqd |
|
90 |
89
|
eleq1d |
|
91 |
|
simpll |
|
92 |
4
|
ssrab3 |
|
93 |
92
|
sseli |
|
94 |
|
r1elssi |
|
95 |
93 94
|
syl |
|
96 |
95
|
sselda |
|
97 |
|
snssi |
|
98 |
43
|
tcss |
|
99 |
97 98
|
syl |
|
100 |
51
|
tcel |
|
101 |
54 100
|
mp1i |
|
102 |
99 101
|
sstrd |
|
103 |
|
ssralv |
|
104 |
102 103
|
syl |
|
105 |
50 104
|
mpan9 |
|
106 |
|
sneq |
|
107 |
106
|
fveq2d |
|
108 |
107
|
raleqdv |
|
109 |
108 4
|
elrab2 |
|
110 |
96 105 109
|
sylanbrc |
|
111 |
110
|
adantll |
|
112 |
111
|
adantll |
|
113 |
90 91 112
|
rspcdva |
|
114 |
|
imassrn |
|
115 |
114 36
|
sstri |
|
116 |
|
fvex |
|
117 |
116
|
funimaex |
|
118 |
42 117
|
ax-mp |
|
119 |
118
|
elpw |
|
120 |
115 119
|
mpbir |
|
121 |
113 120
|
jctil |
|
122 |
121
|
ralrimiva |
|
123 |
|
eqid |
|
124 |
|
eqid |
|
125 |
123 124
|
hsmexlem3 |
|
126 |
81 83 122 125
|
syl21anc |
|
127 |
80 126
|
eqeltrid |
|
128 |
2
|
hsmexlem8 |
|
129 |
128
|
ad2antrl |
|
130 |
127 129
|
eleqtrrd |
|
131 |
130
|
expr |
|
132 |
72 131
|
ralrimi |
|
133 |
132
|
expcom |
|
134 |
14 23 32 69 133
|
finds1 |
|
135 |
134
|
r19.21bi |
|