Step |
Hyp |
Ref |
Expression |
1 |
|
heibor.1 |
|
2 |
1
|
heibor1 |
|
3 |
|
cmetmet |
|
4 |
3
|
adantr |
|
5 |
|
metxmet |
|
6 |
1
|
mopntop |
|
7 |
3 5 6
|
3syl |
|
8 |
7
|
adantr |
|
9 |
|
istotbnd |
|
10 |
9
|
simprbi |
|
11 |
|
2nn |
|
12 |
|
nnexpcl |
|
13 |
11 12
|
mpan |
|
14 |
13
|
nnrpd |
|
15 |
14
|
rpreccld |
|
16 |
|
oveq2 |
|
17 |
16
|
eqeq2d |
|
18 |
17
|
rexbidv |
|
19 |
18
|
ralbidv |
|
20 |
19
|
anbi2d |
|
21 |
20
|
rexbidv |
|
22 |
21
|
rspccva |
|
23 |
10 15 22
|
syl2an |
|
24 |
23
|
expcom |
|
25 |
24
|
adantl |
|
26 |
|
oveq1 |
|
27 |
26
|
eqeq2d |
|
28 |
27
|
ac6sfi |
|
29 |
28
|
adantrl |
|
30 |
29
|
adantl |
|
31 |
|
simp3l |
|
32 |
31
|
frnd |
|
33 |
1
|
mopnuni |
|
34 |
3 5 33
|
3syl |
|
35 |
34
|
adantr |
|
36 |
35
|
3ad2ant1 |
|
37 |
32 36
|
sseqtrd |
|
38 |
1
|
fvexi |
|
39 |
38
|
uniex |
|
40 |
39
|
elpw2 |
|
41 |
37 40
|
sylibr |
|
42 |
|
simp2l |
|
43 |
|
ffn |
|
44 |
|
dffn4 |
|
45 |
43 44
|
sylib |
|
46 |
|
fofi |
|
47 |
45 46
|
sylan2 |
|
48 |
42 31 47
|
syl2anc |
|
49 |
41 48
|
elind |
|
50 |
26
|
eleq2d |
|
51 |
50
|
rexrn |
|
52 |
|
eliun |
|
53 |
|
eliun |
|
54 |
51 52 53
|
3bitr4g |
|
55 |
54
|
eqrdv |
|
56 |
31 43 55
|
3syl |
|
57 |
|
simp3r |
|
58 |
|
uniiun |
|
59 |
|
iuneq2 |
|
60 |
58 59
|
syl5eq |
|
61 |
57 60
|
syl |
|
62 |
|
simp2r |
|
63 |
56 61 62
|
3eqtr2rd |
|
64 |
|
iuneq1 |
|
65 |
64
|
rspceeqv |
|
66 |
49 63 65
|
syl2anc |
|
67 |
66
|
3expia |
|
68 |
67
|
adantrrr |
|
69 |
68
|
exlimdv |
|
70 |
30 69
|
mpd |
|
71 |
70
|
rexlimdvaa |
|
72 |
25 71
|
syld |
|
73 |
72
|
ralrimdva |
|
74 |
39
|
pwex |
|
75 |
74
|
inex1 |
|
76 |
|
nn0ennn |
|
77 |
|
nnenom |
|
78 |
76 77
|
entri |
|
79 |
|
iuneq1 |
|
80 |
79
|
eqeq2d |
|
81 |
75 78 80
|
axcc4 |
|
82 |
73 81
|
syl6 |
|
83 |
|
elpwi |
|
84 |
|
eqid |
|
85 |
|
eqid |
|
86 |
|
eqid |
|
87 |
|
simpl |
|
88 |
34
|
pweqd |
|
89 |
88
|
ineq1d |
|
90 |
89
|
feq3d |
|
91 |
90
|
biimpar |
|
92 |
91
|
adantrr |
|
93 |
|
oveq1 |
|
94 |
93
|
cbviunv |
|
95 |
|
id |
|
96 |
|
inss1 |
|
97 |
96 88
|
sseqtrrid |
|
98 |
|
fss |
|
99 |
95 97 98
|
syl2anr |
|
100 |
99
|
ffvelrnda |
|
101 |
100
|
elpwid |
|
102 |
101
|
sselda |
|
103 |
|
simplr |
|
104 |
|
oveq1 |
|
105 |
|
oveq2 |
|
106 |
105
|
oveq2d |
|
107 |
106
|
oveq2d |
|
108 |
|
ovex |
|
109 |
104 107 86 108
|
ovmpo |
|
110 |
102 103 109
|
syl2anc |
|
111 |
110
|
iuneq2dv |
|
112 |
94 111
|
syl5eq |
|
113 |
112
|
eqeq2d |
|
114 |
113
|
biimprd |
|
115 |
114
|
ralimdva |
|
116 |
115
|
impr |
|
117 |
|
fveq2 |
|
118 |
117
|
iuneq1d |
|
119 |
|
simpl |
|
120 |
119
|
oveq2d |
|
121 |
120
|
iuneq2dv |
|
122 |
118 121
|
eqtrd |
|
123 |
122
|
eqeq2d |
|
124 |
123
|
cbvralvw |
|
125 |
116 124
|
sylib |
|
126 |
1 84 85 86 87 92 125
|
heiborlem10 |
|
127 |
126
|
exp32 |
|
128 |
83 127
|
syl5 |
|
129 |
128
|
ralrimiv |
|
130 |
129
|
ex |
|
131 |
130
|
exlimdv |
|
132 |
82 131
|
syld |
|
133 |
132
|
imp |
|
134 |
|
eqid |
|
135 |
134
|
iscmp |
|
136 |
8 133 135
|
sylanbrc |
|
137 |
4 136
|
jca |
|
138 |
2 137
|
impbii |
|