Step |
Hyp |
Ref |
Expression |
1 |
|
noinfbnd1.1 |
|
2 |
1
|
noinfno |
|
3 |
2
|
3ad2ant2 |
|
4 |
3
|
adantl |
|
5 |
|
nodmord |
|
6 |
4 5
|
syl |
|
7 |
|
ordirr |
|
8 |
6 7
|
syl |
|
9 |
|
simpr3l |
|
10 |
9
|
adantr |
|
11 |
|
ndmfv |
|
12 |
|
2on0 |
|
13 |
12
|
necomi |
|
14 |
|
neeq1 |
|
15 |
13 14
|
mpbiri |
|
16 |
11 15
|
syl |
|
17 |
16
|
neneqd |
|
18 |
17
|
con4i |
|
19 |
18
|
adantl |
|
20 |
|
simpl2l |
|
21 |
20
|
adantr |
|
22 |
|
simpl3l |
|
23 |
22
|
adantr |
|
24 |
21 23
|
sseldd |
|
25 |
|
nofun |
|
26 |
24 25
|
syl |
|
27 |
|
simprll |
|
28 |
21 27
|
sseldd |
|
29 |
|
nofun |
|
30 |
28 29
|
syl |
|
31 |
|
simpl3r |
|
32 |
31
|
adantr |
|
33 |
|
simpll1 |
|
34 |
|
simpll2 |
|
35 |
|
simpll3 |
|
36 |
|
simprl |
|
37 |
1
|
noinfbnd1lem2 |
|
38 |
33 34 35 36 37
|
syl112anc |
|
39 |
32 38
|
eqtr4d |
|
40 |
|
simplr |
|
41 |
40 18
|
syl |
|
42 |
|
simprr |
|
43 |
|
ndmfv |
|
44 |
|
neeq1 |
|
45 |
13 44
|
mpbiri |
|
46 |
43 45
|
syl |
|
47 |
46
|
neneqd |
|
48 |
47
|
con4i |
|
49 |
42 48
|
syl |
|
50 |
40 42
|
eqtr4d |
|
51 |
|
eqfunressuc |
|
52 |
26 30 39 41 49 50 51
|
syl213anc |
|
53 |
52
|
expr |
|
54 |
53
|
expr |
|
55 |
54
|
a2d |
|
56 |
55
|
ralimdva |
|
57 |
56
|
impcom |
|
58 |
57
|
anassrs |
|
59 |
|
dmeq |
|
60 |
59
|
eleq2d |
|
61 |
|
breq1 |
|
62 |
61
|
notbid |
|
63 |
|
reseq1 |
|
64 |
63
|
eqeq1d |
|
65 |
62 64
|
imbi12d |
|
66 |
65
|
ralbidv |
|
67 |
60 66
|
anbi12d |
|
68 |
67
|
rspcev |
|
69 |
10 19 58 68
|
syl12anc |
|
70 |
|
nodmon |
|
71 |
4 70
|
syl |
|
72 |
71
|
adantr |
|
73 |
|
eleq1 |
|
74 |
|
suceq |
|
75 |
74
|
reseq2d |
|
76 |
74
|
reseq2d |
|
77 |
75 76
|
eqeq12d |
|
78 |
77
|
imbi2d |
|
79 |
78
|
ralbidv |
|
80 |
73 79
|
anbi12d |
|
81 |
80
|
rexbidv |
|
82 |
81
|
elabg |
|
83 |
72 82
|
syl |
|
84 |
69 83
|
mpbird |
|
85 |
1
|
noinfdm |
|
86 |
85
|
3ad2ant1 |
|
87 |
86
|
adantl |
|
88 |
87
|
adantr |
|
89 |
88
|
eleq2d |
|
90 |
84 89
|
mpbird |
|
91 |
8 90
|
mtand |
|
92 |
91
|
neqned |
|
93 |
|
rexanali |
|
94 |
|
simpr1 |
|
95 |
|
simpr2 |
|
96 |
|
simplll |
|
97 |
|
simpr3 |
|
98 |
|
simpll |
|
99 |
94 95 97 98 37
|
syl112anc |
|
100 |
1
|
noinfbnd1lem4 |
|
101 |
94 95 96 99 100
|
syl112anc |
|
102 |
101
|
neneqd |
|
103 |
102
|
pm2.21d |
|
104 |
1
|
noinfbnd1lem3 |
|
105 |
94 95 96 99 104
|
syl112anc |
|
106 |
105
|
neneqd |
|
107 |
106
|
pm2.21d |
|
108 |
|
simplr |
|
109 |
|
simpr2l |
|
110 |
109 96
|
sseldd |
|
111 |
|
nofv |
|
112 |
110 111
|
syl |
|
113 |
|
3orel3 |
|
114 |
108 112 113
|
sylc |
|
115 |
103 107 114
|
mpjaod |
|
116 |
115
|
ex |
|
117 |
116
|
anasss |
|
118 |
117
|
rexlimiva |
|
119 |
118
|
imp |
|
120 |
93 119
|
sylanbr |
|
121 |
92 120
|
pm2.61ian |
|