Step |
Hyp |
Ref |
Expression |
1 |
|
noinfbnd2.1 |
|
2 |
|
nfv |
|
3 |
|
nfre1 |
|
4 |
|
nfriota1 |
|
5 |
4
|
nfdm |
|
6 |
|
nfcv |
|
7 |
5 6
|
nfop |
|
8 |
7
|
nfsn |
|
9 |
4 8
|
nfun |
|
10 |
|
nfcv |
|
11 |
|
nfiota1 |
|
12 |
10 11
|
nfmpt |
|
13 |
3 9 12
|
nfif |
|
14 |
1 13
|
nfcxfr |
|
15 |
|
nfcv |
|
16 |
|
nfcv |
|
17 |
14
|
nfdm |
|
18 |
16 17
|
nfres |
|
19 |
14 15 18
|
nfbr |
|
20 |
19
|
nfn |
|
21 |
2 20
|
nfim |
|
22 |
|
noinfbnd2lem1 |
|
23 |
22
|
3expb |
|
24 |
|
rspe |
|
25 |
24
|
adantr |
|
26 |
25
|
iftrued |
|
27 |
|
simpl |
|
28 |
|
simprl1 |
|
29 |
|
nominmo |
|
30 |
28 29
|
syl |
|
31 |
|
reu5 |
|
32 |
25 30 31
|
sylanbrc |
|
33 |
|
riota1 |
|
34 |
32 33
|
syl |
|
35 |
27 34
|
mpbid |
|
36 |
35
|
dmeqd |
|
37 |
36
|
opeq1d |
|
38 |
37
|
sneqd |
|
39 |
35 38
|
uneq12d |
|
40 |
26 39
|
eqtrd |
|
41 |
1 40
|
syl5eq |
|
42 |
41
|
dmeqd |
|
43 |
|
1oex |
|
44 |
43
|
dmsnop |
|
45 |
44
|
uneq2i |
|
46 |
|
dmun |
|
47 |
|
df-suc |
|
48 |
45 46 47
|
3eqtr4ri |
|
49 |
42 48
|
eqtr4di |
|
50 |
49
|
reseq2d |
|
51 |
41 50
|
breq12d |
|
52 |
23 51
|
mtbird |
|
53 |
52
|
exp31 |
|
54 |
21 53
|
rexlimi |
|
55 |
54
|
imp |
|
56 |
|
simprl3 |
|
57 |
1
|
noinfno |
|
58 |
57
|
3adant3 |
|
59 |
58
|
ad2antrl |
|
60 |
|
nodmon |
|
61 |
59 60
|
syl |
|
62 |
|
noreson |
|
63 |
56 61 62
|
syl2anc |
|
64 |
|
nofun |
|
65 |
|
funrel |
|
66 |
58 64 65
|
3syl |
|
67 |
66
|
ad2antrl |
|
68 |
|
resdm |
|
69 |
67 68
|
syl |
|
70 |
69 59
|
eqeltrd |
|
71 |
|
resdmss |
|
72 |
71
|
a1i |
|
73 |
|
resdmss |
|
74 |
73
|
a1i |
|
75 |
1
|
noinfdm |
|
76 |
75
|
abeq2d |
|
77 |
76
|
adantr |
|
78 |
|
simpll |
|
79 |
|
simprl1 |
|
80 |
79
|
adantr |
|
81 |
|
simprl2 |
|
82 |
81
|
adantr |
|
83 |
|
simprl |
|
84 |
|
simprrl |
|
85 |
|
simprrr |
|
86 |
|
breq2 |
|
87 |
86
|
notbid |
|
88 |
|
reseq1 |
|
89 |
88
|
eqeq2d |
|
90 |
87 89
|
imbi12d |
|
91 |
90
|
cbvralvw |
|
92 |
85 91
|
sylib |
|
93 |
1
|
noinfres |
|
94 |
78 80 82 83 84 92 93
|
syl123anc |
|
95 |
|
breq2 |
|
96 |
|
simplrr |
|
97 |
95 96 83
|
rspcdva |
|
98 |
56
|
adantr |
|
99 |
80 83
|
sseldd |
|
100 |
|
sltso |
|
101 |
|
soasym |
|
102 |
100 101
|
mpan |
|
103 |
98 99 102
|
syl2anc |
|
104 |
97 103
|
mpd |
|
105 |
|
nodmon |
|
106 |
99 105
|
syl |
|
107 |
|
onelon |
|
108 |
106 84 107
|
syl2anc |
|
109 |
|
sucelon |
|
110 |
108 109
|
sylib |
|
111 |
|
sltres |
|
112 |
99 98 110 111
|
syl3anc |
|
113 |
104 112
|
mtod |
|
114 |
94 113
|
eqnbrtrd |
|
115 |
114
|
rexlimdvaa |
|
116 |
77 115
|
sylbid |
|
117 |
116
|
imp |
|
118 |
|
nodmord |
|
119 |
|
ordsucss |
|
120 |
59 118 119
|
3syl |
|
121 |
120
|
imp |
|
122 |
121
|
resabs1d |
|
123 |
121
|
resabs1d |
|
124 |
122 123
|
breq12d |
|
125 |
117 124
|
mtbird |
|
126 |
125
|
ralrimiva |
|
127 |
|
noresle |
|
128 |
63 70 72 74 126 127
|
syl23anc |
|
129 |
69
|
breq1d |
|
130 |
128 129
|
mtbid |
|
131 |
55 130
|
pm2.61ian |
|
132 |
|
simplr |
|
133 |
|
simpll1 |
|
134 |
|
simpll2 |
|
135 |
|
simpr |
|
136 |
1
|
noinfbnd1 |
|
137 |
133 134 135 136
|
syl3anc |
|
138 |
|
simpl3 |
|
139 |
|
simpl1 |
|
140 |
|
simpl2 |
|
141 |
139 140 57
|
syl2anc |
|
142 |
141 60
|
syl |
|
143 |
138 142 62
|
syl2anc |
|
144 |
143
|
adantr |
|
145 |
141
|
adantr |
|
146 |
139
|
sselda |
|
147 |
142
|
adantr |
|
148 |
|
noreson |
|
149 |
146 147 148
|
syl2anc |
|
150 |
|
sotr2 |
|
151 |
100 150
|
mpan |
|
152 |
144 145 149 151
|
syl3anc |
|
153 |
132 137 152
|
mp2and |
|
154 |
|
simpll3 |
|
155 |
|
sltres |
|
156 |
154 146 147 155
|
syl3anc |
|
157 |
153 156
|
mpd |
|
158 |
157
|
ralrimiva |
|
159 |
131 158
|
impbida |
|