Step |
Hyp |
Ref |
Expression |
1 |
|
iblabsnc.1 |
|
2 |
|
iblabsnc.2 |
|
3 |
|
iblabsnclem.1 |
|
4 |
|
iblabsnclem.2 |
|
5 |
|
iblabsnclem.3 |
|
6 |
5
|
iblrelem |
|
7 |
4 6
|
mpbid |
|
8 |
7
|
simp1d |
|
9 |
8 5
|
mbfdm2 |
|
10 |
|
mblss |
|
11 |
9 10
|
syl |
|
12 |
|
rembl |
|
13 |
12
|
a1i |
|
14 |
5
|
recnd |
|
15 |
14
|
abscld |
|
16 |
|
0re |
|
17 |
|
ifcl |
|
18 |
15 16 17
|
sylancl |
|
19 |
|
eldifn |
|
20 |
19
|
adantl |
|
21 |
|
iffalse |
|
22 |
20 21
|
syl |
|
23 |
|
iftrue |
|
24 |
23
|
mpteq2ia |
|
25 |
15
|
fmpttd |
|
26 |
15
|
adantlr |
|
27 |
26
|
biantrurd |
|
28 |
5
|
adantlr |
|
29 |
|
simplr |
|
30 |
28 29
|
absled |
|
31 |
30
|
notbid |
|
32 |
29 26
|
ltnled |
|
33 |
|
renegcl |
|
34 |
33
|
rexrd |
|
35 |
34
|
ad2antlr |
|
36 |
|
elioomnf |
|
37 |
35 36
|
syl |
|
38 |
28
|
biantrurd |
|
39 |
29
|
renegcld |
|
40 |
28 39
|
ltnled |
|
41 |
37 38 40
|
3bitr2d |
|
42 |
|
rexr |
|
43 |
42
|
ad2antlr |
|
44 |
|
elioopnf |
|
45 |
43 44
|
syl |
|
46 |
28
|
biantrurd |
|
47 |
29 28
|
ltnled |
|
48 |
45 46 47
|
3bitr2d |
|
49 |
41 48
|
orbi12d |
|
50 |
|
ianor |
|
51 |
49 50
|
bitr4di |
|
52 |
31 32 51
|
3bitr4rd |
|
53 |
|
elioopnf |
|
54 |
43 53
|
syl |
|
55 |
27 52 54
|
3bitr4rd |
|
56 |
55
|
rabbidva |
|
57 |
|
eqid |
|
58 |
57
|
mptpreima |
|
59 |
|
eqid |
|
60 |
59
|
mptpreima |
|
61 |
59
|
mptpreima |
|
62 |
60 61
|
uneq12i |
|
63 |
|
unrab |
|
64 |
62 63
|
eqtri |
|
65 |
56 58 64
|
3eqtr4g |
|
66 |
|
iblmbf |
|
67 |
4 66
|
syl |
|
68 |
5
|
fmpttd |
|
69 |
|
mbfima |
|
70 |
|
mbfima |
|
71 |
|
unmbl |
|
72 |
69 70 71
|
syl2anc |
|
73 |
67 68 72
|
syl2anc |
|
74 |
73
|
adantr |
|
75 |
65 74
|
eqeltrd |
|
76 |
|
elioomnf |
|
77 |
43 76
|
syl |
|
78 |
26
|
biantrurd |
|
79 |
28 29
|
absltd |
|
80 |
77 78 79
|
3bitr2d |
|
81 |
28
|
biantrurd |
|
82 |
80 81
|
bitrd |
|
83 |
|
3anass |
|
84 |
82 83
|
bitr4di |
|
85 |
|
elioo2 |
|
86 |
34 42 85
|
syl2anc |
|
87 |
86
|
ad2antlr |
|
88 |
84 87
|
bitr4d |
|
89 |
88
|
rabbidva |
|
90 |
57
|
mptpreima |
|
91 |
59
|
mptpreima |
|
92 |
89 90 91
|
3eqtr4g |
|
93 |
|
mbfima |
|
94 |
67 68 93
|
syl2anc |
|
95 |
94
|
adantr |
|
96 |
92 95
|
eqeltrd |
|
97 |
25 9 75 96
|
ismbf2d |
|
98 |
24 97
|
eqeltrid |
|
99 |
11 13 18 22 98
|
mbfss |
|
100 |
3 99
|
eqeltrid |
|
101 |
|
reex |
|
102 |
101
|
a1i |
|
103 |
|
ifan |
|
104 |
|
ifcl |
|
105 |
5 16 104
|
sylancl |
|
106 |
|
max1 |
|
107 |
16 5 106
|
sylancr |
|
108 |
|
elrege0 |
|
109 |
105 107 108
|
sylanbrc |
|
110 |
|
0e0icopnf |
|
111 |
110
|
a1i |
|
112 |
109 111
|
ifclda |
|
113 |
103 112
|
eqeltrid |
|
114 |
113
|
adantr |
|
115 |
|
ifan |
|
116 |
5
|
renegcld |
|
117 |
|
ifcl |
|
118 |
116 16 117
|
sylancl |
|
119 |
|
max1 |
|
120 |
16 116 119
|
sylancr |
|
121 |
|
elrege0 |
|
122 |
118 120 121
|
sylanbrc |
|
123 |
122 111
|
ifclda |
|
124 |
115 123
|
eqeltrid |
|
125 |
124
|
adantr |
|
126 |
|
eqidd |
|
127 |
|
eqidd |
|
128 |
102 114 125 126 127
|
offval2 |
|
129 |
103 115
|
oveq12i |
|
130 |
|
max0add |
|
131 |
5 130
|
syl |
|
132 |
|
iftrue |
|
133 |
132
|
adantl |
|
134 |
|
iftrue |
|
135 |
134
|
adantl |
|
136 |
133 135
|
oveq12d |
|
137 |
23
|
adantl |
|
138 |
131 136 137
|
3eqtr4d |
|
139 |
138
|
ex |
|
140 |
|
00id |
|
141 |
|
iffalse |
|
142 |
|
iffalse |
|
143 |
141 142
|
oveq12d |
|
144 |
140 143 21
|
3eqtr4a |
|
145 |
139 144
|
pm2.61d1 |
|
146 |
129 145
|
syl5eq |
|
147 |
146
|
mpteq2dv |
|
148 |
128 147
|
eqtrd |
|
149 |
3 148
|
eqtr4id |
|
150 |
149
|
fveq2d |
|
151 |
113
|
adantr |
|
152 |
103 141
|
syl5eq |
|
153 |
20 152
|
syl |
|
154 |
|
ibar |
|
155 |
154
|
ifbid |
|
156 |
155
|
mpteq2ia |
|
157 |
5 8
|
mbfpos |
|
158 |
156 157
|
eqeltrrid |
|
159 |
11 13 151 153 158
|
mbfss |
|
160 |
114
|
fmpttd |
|
161 |
7
|
simp2d |
|
162 |
125
|
fmpttd |
|
163 |
7
|
simp3d |
|
164 |
159 160 161 162 163
|
itg2addnc |
|
165 |
150 164
|
eqtrd |
|
166 |
161 163
|
readdcld |
|
167 |
165 166
|
eqeltrd |
|
168 |
100 167
|
jca |
|