Step |
Hyp |
Ref |
Expression |
1 |
|
noreson |
|
2 |
1
|
3adant2 |
|
3 |
|
noreson |
|
4 |
3
|
3adant1 |
|
5 |
|
sltintdifex |
|
6 |
|
onintrab |
|
7 |
5 6
|
syl6ib |
|
8 |
2 4 7
|
syl2anc |
|
9 |
8
|
imp |
|
10 |
|
simpl3 |
|
11 |
|
sltval2 |
|
12 |
2 4 11
|
syl2anc |
|
13 |
|
fvex |
|
14 |
|
fvex |
|
15 |
13 14
|
brtp |
|
16 |
|
1n0 |
|
17 |
16
|
neii |
|
18 |
|
eqeq1 |
|
19 |
17 18
|
mtbiri |
|
20 |
|
ndmfv |
|
21 |
19 20
|
nsyl2 |
|
22 |
21
|
adantr |
|
23 |
22
|
orcd |
|
24 |
21
|
adantr |
|
25 |
24
|
orcd |
|
26 |
|
2on |
|
27 |
26
|
elexi |
|
28 |
27
|
prid2 |
|
29 |
28
|
nosgnn0i |
|
30 |
29
|
neii |
|
31 |
|
eqeq1 |
|
32 |
|
eqcom |
|
33 |
31 32
|
bitrdi |
|
34 |
30 33
|
mtbiri |
|
35 |
|
ndmfv |
|
36 |
34 35
|
nsyl2 |
|
37 |
36
|
adantl |
|
38 |
37
|
olcd |
|
39 |
23 25 38
|
3jaoi |
|
40 |
15 39
|
sylbi |
|
41 |
12 40
|
syl6bi |
|
42 |
41
|
imp |
|
43 |
|
dmres |
|
44 |
43
|
elin2 |
|
45 |
44
|
simplbi |
|
46 |
|
dmres |
|
47 |
46
|
elin2 |
|
48 |
47
|
simplbi |
|
49 |
45 48
|
jaoi |
|
50 |
42 49
|
syl |
|
51 |
|
onelss |
|
52 |
10 50 51
|
sylc |
|
53 |
52
|
sselda |
|
54 |
|
onelon |
|
55 |
9 54
|
sylan |
|
56 |
|
intss1 |
|
57 |
|
ontri1 |
|
58 |
56 57
|
syl5ib |
|
59 |
58
|
con2d |
|
60 |
9 59
|
sylan |
|
61 |
60
|
impancom |
|
62 |
55 61
|
mpd |
|
63 |
|
fveq2 |
|
64 |
|
fveq2 |
|
65 |
63 64
|
neeq12d |
|
66 |
65
|
elrab |
|
67 |
66
|
simplbi2 |
|
68 |
67
|
con3d |
|
69 |
55 62 68
|
sylc |
|
70 |
|
df-ne |
|
71 |
70
|
con2bii |
|
72 |
69 71
|
sylibr |
|
73 |
|
fvres |
|
74 |
|
fvres |
|
75 |
73 74
|
eqeq12d |
|
76 |
75
|
biimpd |
|
77 |
53 72 76
|
sylc |
|
78 |
77
|
ralrimiva |
|
79 |
|
fvresval |
|
80 |
79
|
ori |
|
81 |
19 80
|
nsyl2 |
|
82 |
81
|
eqcomd |
|
83 |
|
eqeq2 |
|
84 |
82 83
|
mpbid |
|
85 |
84
|
adantr |
|
86 |
85
|
a1i |
|
87 |
21
|
ad2antrl |
|
88 |
87 45
|
syl |
|
89 |
|
nofun |
|
90 |
|
fvelrn |
|
91 |
90
|
ex |
|
92 |
89 91
|
syl |
|
93 |
|
norn |
|
94 |
93
|
sseld |
|
95 |
92 94
|
syld |
|
96 |
|
nosgnn0 |
|
97 |
|
eleq1 |
|
98 |
96 97
|
mtbiri |
|
99 |
95 98
|
nsyli |
|
100 |
4 99
|
syl |
|
101 |
100
|
imp |
|
102 |
101
|
adantrl |
|
103 |
47
|
simplbi2 |
|
104 |
103
|
con3d |
|
105 |
88 102 104
|
sylc |
|
106 |
|
ndmfv |
|
107 |
105 106
|
syl |
|
108 |
107
|
ex |
|
109 |
86 108
|
jcad |
|
110 |
|
fvresval |
|
111 |
110
|
ori |
|
112 |
34 111
|
nsyl2 |
|
113 |
112
|
eqcomd |
|
114 |
|
eqeq2 |
|
115 |
113 114
|
mpbid |
|
116 |
84 115
|
anim12i |
|
117 |
116
|
a1i |
|
118 |
36
|
ad2antll |
|
119 |
118 48
|
syl |
|
120 |
|
nofun |
|
121 |
|
fvelrn |
|
122 |
121
|
ex |
|
123 |
120 122
|
syl |
|
124 |
|
norn |
|
125 |
124
|
sseld |
|
126 |
123 125
|
syld |
|
127 |
|
eleq1 |
|
128 |
96 127
|
mtbiri |
|
129 |
126 128
|
nsyli |
|
130 |
2 129
|
syl |
|
131 |
130
|
imp |
|
132 |
131
|
adantrr |
|
133 |
44
|
simplbi2 |
|
134 |
133
|
con3d |
|
135 |
119 132 134
|
sylc |
|
136 |
135
|
ex |
|
137 |
|
ndmfv |
|
138 |
136 137
|
syl6 |
|
139 |
115
|
adantl |
|
140 |
139
|
a1i |
|
141 |
138 140
|
jcad |
|
142 |
109 117 141
|
3orim123d |
|
143 |
|
fvex |
|
144 |
|
fvex |
|
145 |
143 144
|
brtp |
|
146 |
142 15 145
|
3imtr4g |
|
147 |
12 146
|
sylbid |
|
148 |
147
|
imp |
|
149 |
|
raleq |
|
150 |
|
fveq2 |
|
151 |
|
fveq2 |
|
152 |
150 151
|
breq12d |
|
153 |
149 152
|
anbi12d |
|
154 |
153
|
rspcev |
|
155 |
9 78 148 154
|
syl12anc |
|
156 |
|
sltval |
|
157 |
156
|
3adant3 |
|
158 |
157
|
adantr |
|
159 |
155 158
|
mpbird |
|
160 |
159
|
ex |
|