Step |
Hyp |
Ref |
Expression |
1 |
|
br8.1 |
|
2 |
|
br8.2 |
|
3 |
|
br8.3 |
|
4 |
|
br8.4 |
|
5 |
|
br8.5 |
|
6 |
|
br8.6 |
|
7 |
|
br8.7 |
|
8 |
|
br8.8 |
|
9 |
|
br8.9 |
|
10 |
|
br8.10 |
|
11 |
|
opex |
|
12 |
|
opex |
|
13 |
|
eqeq1 |
|
14 |
13
|
3anbi1d |
|
15 |
14
|
rexbidv |
|
16 |
15
|
2rexbidv |
|
17 |
16
|
2rexbidv |
|
18 |
17
|
2rexbidv |
|
19 |
18
|
2rexbidv |
|
20 |
|
eqeq1 |
|
21 |
20
|
3anbi2d |
|
22 |
21
|
rexbidv |
|
23 |
22
|
2rexbidv |
|
24 |
23
|
2rexbidv |
|
25 |
24
|
2rexbidv |
|
26 |
25
|
2rexbidv |
|
27 |
11 12 19 26 10
|
brab |
|
28 |
|
opex |
|
29 |
|
opex |
|
30 |
28 29
|
opth |
|
31 |
|
vex |
|
32 |
|
vex |
|
33 |
31 32
|
opth |
|
34 |
1 2
|
sylan9bb |
|
35 |
33 34
|
sylbi |
|
36 |
|
vex |
|
37 |
|
vex |
|
38 |
36 37
|
opth |
|
39 |
3 4
|
sylan9bb |
|
40 |
38 39
|
sylbi |
|
41 |
35 40
|
sylan9bb |
|
42 |
30 41
|
sylbi |
|
43 |
42
|
eqcoms |
|
44 |
|
opex |
|
45 |
|
opex |
|
46 |
44 45
|
opth |
|
47 |
|
vex |
|
48 |
|
vex |
|
49 |
47 48
|
opth |
|
50 |
5 6
|
sylan9bb |
|
51 |
49 50
|
sylbi |
|
52 |
|
vex |
|
53 |
|
vex |
|
54 |
52 53
|
opth |
|
55 |
7 8
|
sylan9bb |
|
56 |
54 55
|
sylbi |
|
57 |
51 56
|
sylan9bb |
|
58 |
46 57
|
sylbi |
|
59 |
58
|
eqcoms |
|
60 |
43 59
|
sylan9bb |
|
61 |
60
|
biimp3a |
|
62 |
61
|
a1i |
|
63 |
62
|
rexlimdva |
|
64 |
63
|
rexlimdvva |
|
65 |
64
|
rexlimdvva |
|
66 |
65
|
rexlimdvva |
|
67 |
66
|
rexlimdvva |
|
68 |
|
simpl11 |
|
69 |
|
simpl12 |
|
70 |
|
simpl13 |
|
71 |
|
simpl21 |
|
72 |
|
simpl22 |
|
73 |
|
simpl23 |
|
74 |
|
simpl31 |
|
75 |
|
simpl32 |
|
76 |
|
simpl33 |
|
77 |
|
eqidd |
|
78 |
|
eqidd |
|
79 |
|
simpr |
|
80 |
|
opeq1 |
|
81 |
80
|
opeq2d |
|
82 |
81
|
eqeq2d |
|
83 |
82 7
|
3anbi23d |
|
84 |
|
opeq2 |
|
85 |
84
|
opeq2d |
|
86 |
85
|
eqeq2d |
|
87 |
86 8
|
3anbi23d |
|
88 |
83 87
|
rspc2ev |
|
89 |
75 76 77 78 79 88
|
syl113anc |
|
90 |
|
opeq2 |
|
91 |
90
|
opeq2d |
|
92 |
91
|
eqeq2d |
|
93 |
92 4
|
3anbi13d |
|
94 |
93
|
2rexbidv |
|
95 |
|
opeq1 |
|
96 |
95
|
opeq1d |
|
97 |
96
|
eqeq2d |
|
98 |
97 5
|
3anbi23d |
|
99 |
98
|
2rexbidv |
|
100 |
|
opeq2 |
|
101 |
100
|
opeq1d |
|
102 |
101
|
eqeq2d |
|
103 |
102 6
|
3anbi23d |
|
104 |
103
|
2rexbidv |
|
105 |
94 99 104
|
rspc3ev |
|
106 |
72 73 74 89 105
|
syl31anc |
|
107 |
|
opeq1 |
|
108 |
107
|
opeq1d |
|
109 |
108
|
eqeq2d |
|
110 |
109 1
|
3anbi13d |
|
111 |
110
|
rexbidv |
|
112 |
111
|
2rexbidv |
|
113 |
112
|
2rexbidv |
|
114 |
|
opeq2 |
|
115 |
114
|
opeq1d |
|
116 |
115
|
eqeq2d |
|
117 |
116 2
|
3anbi13d |
|
118 |
117
|
rexbidv |
|
119 |
118
|
2rexbidv |
|
120 |
119
|
2rexbidv |
|
121 |
|
opeq1 |
|
122 |
121
|
opeq2d |
|
123 |
122
|
eqeq2d |
|
124 |
123 3
|
3anbi13d |
|
125 |
124
|
rexbidv |
|
126 |
125
|
2rexbidv |
|
127 |
126
|
2rexbidv |
|
128 |
113 120 127
|
rspc3ev |
|
129 |
69 70 71 106 128
|
syl31anc |
|
130 |
9
|
rexeqdv |
|
131 |
9 130
|
rexeqbidv |
|
132 |
9 131
|
rexeqbidv |
|
133 |
9 132
|
rexeqbidv |
|
134 |
9 133
|
rexeqbidv |
|
135 |
9 134
|
rexeqbidv |
|
136 |
9 135
|
rexeqbidv |
|
137 |
9 136
|
rexeqbidv |
|
138 |
137
|
rspcev |
|
139 |
68 129 138
|
syl2anc |
|
140 |
139
|
ex |
|
141 |
67 140
|
impbid |
|
142 |
27 141
|
syl5bb |
|