Step |
Hyp |
Ref |
Expression |
1 |
|
noinfres.1 |
|
2 |
|
dmres |
|
3 |
1
|
noinfno |
|
4 |
3
|
3ad2ant2 |
|
5 |
|
nodmord |
|
6 |
4 5
|
syl |
|
7 |
|
simp31 |
|
8 |
|
simp32 |
|
9 |
|
simp33 |
|
10 |
|
dmeq |
|
11 |
10
|
eleq2d |
|
12 |
|
breq1 |
|
13 |
12
|
notbid |
|
14 |
|
reseq1 |
|
15 |
14
|
eqeq1d |
|
16 |
13 15
|
imbi12d |
|
17 |
16
|
ralbidv |
|
18 |
|
breq2 |
|
19 |
18
|
notbid |
|
20 |
|
reseq1 |
|
21 |
20
|
eqeq2d |
|
22 |
19 21
|
imbi12d |
|
23 |
22
|
cbvralvw |
|
24 |
17 23
|
bitrdi |
|
25 |
11 24
|
anbi12d |
|
26 |
25
|
rspcev |
|
27 |
7 8 9 26
|
syl12anc |
|
28 |
|
eleq1 |
|
29 |
|
suceq |
|
30 |
29
|
reseq2d |
|
31 |
29
|
reseq2d |
|
32 |
30 31
|
eqeq12d |
|
33 |
32
|
imbi2d |
|
34 |
33
|
ralbidv |
|
35 |
28 34
|
anbi12d |
|
36 |
35
|
rexbidv |
|
37 |
36
|
elabg |
|
38 |
8 37
|
syl |
|
39 |
27 38
|
mpbird |
|
40 |
1
|
noinfdm |
|
41 |
40
|
3ad2ant1 |
|
42 |
39 41
|
eleqtrrd |
|
43 |
|
ordsucss |
|
44 |
6 42 43
|
sylc |
|
45 |
|
df-ss |
|
46 |
44 45
|
sylib |
|
47 |
2 46
|
syl5eq |
|
48 |
|
dmres |
|
49 |
|
simp2l |
|
50 |
49 7
|
sseldd |
|
51 |
|
nodmon |
|
52 |
50 51
|
syl |
|
53 |
|
eloni |
|
54 |
52 53
|
syl |
|
55 |
|
ordsucss |
|
56 |
54 8 55
|
sylc |
|
57 |
|
df-ss |
|
58 |
56 57
|
sylib |
|
59 |
48 58
|
syl5eq |
|
60 |
47 59
|
eqtr4d |
|
61 |
47
|
eleq2d |
|
62 |
|
simpl1 |
|
63 |
|
simpl2 |
|
64 |
|
simpl31 |
|
65 |
56
|
sselda |
|
66 |
50
|
adantr |
|
67 |
66 51
|
syl |
|
68 |
|
simpl32 |
|
69 |
|
onelon |
|
70 |
67 68 69
|
syl2anc |
|
71 |
|
sucelon |
|
72 |
70 71
|
sylib |
|
73 |
|
eloni |
|
74 |
72 73
|
syl |
|
75 |
|
simpr |
|
76 |
|
ordsucss |
|
77 |
74 75 76
|
sylc |
|
78 |
|
simpl33 |
|
79 |
|
reseq1 |
|
80 |
|
resabs1 |
|
81 |
|
resabs1 |
|
82 |
80 81
|
eqeq12d |
|
83 |
79 82
|
syl5ib |
|
84 |
83
|
imim2d |
|
85 |
84
|
ralimdv |
|
86 |
77 78 85
|
sylc |
|
87 |
1
|
noinffv |
|
88 |
62 63 64 65 86 87
|
syl113anc |
|
89 |
75
|
fvresd |
|
90 |
75
|
fvresd |
|
91 |
88 89 90
|
3eqtr4d |
|
92 |
91
|
ex |
|
93 |
61 92
|
sylbid |
|
94 |
93
|
ralrimiv |
|
95 |
|
nofun |
|
96 |
95
|
funresd |
|
97 |
4 96
|
syl |
|
98 |
|
nofun |
|
99 |
98
|
funresd |
|
100 |
50 99
|
syl |
|
101 |
|
eqfunfv |
|
102 |
97 100 101
|
syl2anc |
|
103 |
60 94 102
|
mpbir2and |
|