Step |
Hyp |
Ref |
Expression |
1 |
|
heibor.1 |
|
2 |
|
heibor.3 |
|
3 |
|
heibor.4 |
|
4 |
|
heibor.5 |
|
5 |
|
heibor.6 |
|
6 |
|
heibor.7 |
|
7 |
|
heibor.8 |
|
8 |
|
0nn0 |
|
9 |
|
inss2 |
|
10 |
|
ffvelrn |
|
11 |
9 10
|
sseldi |
|
12 |
6 8 11
|
sylancl |
|
13 |
|
fveq2 |
|
14 |
|
oveq2 |
|
15 |
13 14
|
iuneq12d |
|
16 |
15
|
eqeq2d |
|
17 |
16
|
rspccva |
|
18 |
7 8 17
|
sylancl |
|
19 |
|
eqimss |
|
20 |
18 19
|
syl |
|
21 |
|
ovex |
|
22 |
1 2 21
|
heiborlem1 |
|
23 |
|
oveq1 |
|
24 |
23
|
eleq1d |
|
25 |
24
|
cbvrexvw |
|
26 |
22 25
|
sylib |
|
27 |
26
|
3expia |
|
28 |
12 20 27
|
syl2anc |
|
29 |
28
|
adantr |
|
30 |
|
vex |
|
31 |
|
c0ex |
|
32 |
1 2 3 30 31
|
heiborlem2 |
|
33 |
1 2 3 4 5 6 7
|
heiborlem3 |
|
34 |
33
|
ad2antrr |
|
35 |
5
|
ad2antrr |
|
36 |
6
|
ad2antrr |
|
37 |
7
|
ad2antrr |
|
38 |
|
simprr |
|
39 |
|
fveq2 |
|
40 |
|
fveq2 |
|
41 |
40
|
oveq1d |
|
42 |
39 41
|
breq12d |
|
43 |
|
fveq2 |
|
44 |
39 41
|
oveq12d |
|
45 |
43 44
|
ineq12d |
|
46 |
45
|
eleq1d |
|
47 |
42 46
|
anbi12d |
|
48 |
47
|
cbvralvw |
|
49 |
38 48
|
sylib |
|
50 |
|
simprl |
|
51 |
|
eqeq1 |
|
52 |
|
oveq1 |
|
53 |
51 52
|
ifbieq2d |
|
54 |
53
|
cbvmptv |
|
55 |
|
seqeq3 |
|
56 |
54 55
|
ax-mp |
|
57 |
|
eqid |
|
58 |
|
simplrl |
|
59 |
|
cmetmet |
|
60 |
|
metxmet |
|
61 |
1
|
mopnuni |
|
62 |
5 59 60 61
|
4syl |
|
63 |
62
|
adantr |
|
64 |
|
simprr |
|
65 |
63 64
|
eqtr2d |
|
66 |
65
|
adantr |
|
67 |
1 2 3 4 35 36 37 49 50 56 57 58 66
|
heiborlem9 |
|
68 |
67
|
expr |
|
69 |
68
|
exlimdv |
|
70 |
34 69
|
mpd |
|
71 |
32 70
|
sylan2br |
|
72 |
71
|
3exp2 |
|
73 |
8 72
|
mpi |
|
74 |
73
|
rexlimdv |
|
75 |
29 74
|
syld |
|
76 |
75
|
pm2.01d |
|
77 |
|
elfvdm |
|
78 |
|
sseq1 |
|
79 |
78
|
rexbidv |
|
80 |
79
|
notbid |
|
81 |
80 2
|
elab2g |
|
82 |
5 77 81
|
3syl |
|
83 |
82
|
adantr |
|
84 |
83
|
con2bid |
|
85 |
76 84
|
mpbird |
|
86 |
62
|
ad2antrr |
|
87 |
86
|
sseq1d |
|
88 |
|
inss1 |
|
89 |
88
|
sseli |
|
90 |
89
|
elpwid |
|
91 |
|
simprl |
|
92 |
|
sstr |
|
93 |
92
|
unissd |
|
94 |
90 91 93
|
syl2anr |
|
95 |
94
|
biantrud |
|
96 |
|
eqss |
|
97 |
95 96
|
bitr4di |
|
98 |
87 97
|
bitrd |
|
99 |
98
|
rexbidva |
|
100 |
85 99
|
mpbid |
|