Step |
Hyp |
Ref |
Expression |
1 |
|
isomennd.x |
|
2 |
|
isomennd.o |
|
3 |
|
isomennd.o0 |
|
4 |
|
isomennd.le |
|
5 |
|
isomennd.sa |
|
6 |
|
id |
|
7 |
|
fdm |
|
8 |
7
|
feq2d |
|
9 |
6 8
|
mpbird |
|
10 |
2 9
|
syl |
|
11 |
|
unipw |
|
12 |
11
|
pweqi |
|
13 |
12
|
a1i |
|
14 |
2 7
|
syl |
|
15 |
14
|
unieqd |
|
16 |
15
|
pweqd |
|
17 |
13 16 14
|
3eqtr4rd |
|
18 |
10 17 3
|
jca31 |
|
19 |
|
simpl |
|
20 |
|
simpr |
|
21 |
16 13
|
eqtrd |
|
22 |
21
|
adantr |
|
23 |
20 22
|
eleqtrd |
|
24 |
|
elpwi |
|
25 |
23 24
|
syl |
|
26 |
25
|
adantrr |
|
27 |
|
elpwi |
|
28 |
27
|
adantl |
|
29 |
28
|
adantl |
|
30 |
19 26 29 4
|
syl3anc |
|
31 |
30
|
ralrimivva |
|
32 |
|
0le0 |
|
33 |
32
|
a1i |
|
34 |
|
unieq |
|
35 |
|
uni0 |
|
36 |
35
|
a1i |
|
37 |
34 36
|
eqtrd |
|
38 |
37
|
fveq2d |
|
39 |
38
|
adantl |
|
40 |
3
|
adantr |
|
41 |
39 40
|
eqtrd |
|
42 |
|
reseq2 |
|
43 |
|
res0 |
|
44 |
43
|
a1i |
|
45 |
42 44
|
eqtrd |
|
46 |
45
|
fveq2d |
|
47 |
|
sge00 |
|
48 |
47
|
a1i |
|
49 |
46 48
|
eqtrd |
|
50 |
49
|
adantl |
|
51 |
41 50
|
breq12d |
|
52 |
33 51
|
mpbird |
|
53 |
52
|
ad4ant14 |
|
54 |
|
simpl |
|
55 |
|
neqne |
|
56 |
55
|
adantl |
|
57 |
|
ssnnf1octb |
|
58 |
57
|
adantll |
|
59 |
2
|
ad2antrr |
|
60 |
3
|
ad2antrr |
|
61 |
|
simpr |
|
62 |
14
|
pweqd |
|
63 |
62
|
adantr |
|
64 |
61 63
|
eleqtrd |
|
65 |
|
elpwi |
|
66 |
64 65
|
syl |
|
67 |
66
|
adantr |
|
68 |
|
simpl |
|
69 |
68 5
|
sylan |
|
70 |
69
|
adantlr |
|
71 |
|
simprl |
|
72 |
|
simprr |
|
73 |
|
eleq1w |
|
74 |
|
fveq2 |
|
75 |
73 74
|
ifbieq1d |
|
76 |
75
|
cbvmptv |
|
77 |
59 60 67 70 71 72 76
|
isomenndlem |
|
78 |
77
|
ex |
|
79 |
78
|
ad2antrr |
|
80 |
79
|
exlimdv |
|
81 |
58 80
|
mpd |
|
82 |
54 56 81
|
syl2anc |
|
83 |
53 82
|
pm2.61dan |
|
84 |
83
|
ex |
|
85 |
84
|
ralrimiva |
|
86 |
18 31 85
|
jca31 |
|
87 |
1
|
pwexd |
|
88 |
|
fex |
|
89 |
2 87 88
|
syl2anc |
|
90 |
|
isome |
|
91 |
89 90
|
syl |
|
92 |
86 91
|
mpbird |
|