Step |
Hyp |
Ref |
Expression |
1 |
|
xpord2.1 |
|
2 |
|
frxp2.1 |
|
3 |
|
frxp2.2 |
|
4 |
|
dmss |
|
5 |
4
|
ad2antrl |
|
6 |
|
dmxpss |
|
7 |
5 6
|
sstrdi |
|
8 |
|
simprr |
|
9 |
|
relxp |
|
10 |
|
relss |
|
11 |
9 10
|
mpi |
|
12 |
11
|
ad2antrl |
|
13 |
|
reldm0 |
|
14 |
12 13
|
syl |
|
15 |
14
|
necon3bid |
|
16 |
8 15
|
mpbid |
|
17 |
2
|
adantr |
|
18 |
|
df-fr |
|
19 |
17 18
|
sylib |
|
20 |
|
vex |
|
21 |
20
|
dmex |
|
22 |
|
sseq1 |
|
23 |
|
neeq1 |
|
24 |
22 23
|
anbi12d |
|
25 |
|
raleq |
|
26 |
25
|
rexeqbi1dv |
|
27 |
24 26
|
imbi12d |
|
28 |
21 27
|
spcv |
|
29 |
19 28
|
syl |
|
30 |
7 16 29
|
mp2and |
|
31 |
|
imassrn |
|
32 |
|
rnss |
|
33 |
32
|
ad2antrl |
|
34 |
33
|
adantr |
|
35 |
|
rnxpss |
|
36 |
34 35
|
sstrdi |
|
37 |
31 36
|
sstrid |
|
38 |
|
simprl |
|
39 |
|
imadisj |
|
40 |
|
disjsn |
|
41 |
39 40
|
bitri |
|
42 |
41
|
necon2abii |
|
43 |
38 42
|
sylib |
|
44 |
|
df-fr |
|
45 |
3 44
|
sylib |
|
46 |
45
|
ad2antrr |
|
47 |
20
|
imaex |
|
48 |
|
sseq1 |
|
49 |
|
neeq1 |
|
50 |
48 49
|
anbi12d |
|
51 |
|
raleq |
|
52 |
51
|
rexeqbi1dv |
|
53 |
50 52
|
imbi12d |
|
54 |
47 53
|
spcv |
|
55 |
46 54
|
syl |
|
56 |
37 43 55
|
mp2and |
|
57 |
|
simprl |
|
58 |
|
vex |
|
59 |
|
vex |
|
60 |
58 59
|
elimasn |
|
61 |
57 60
|
sylib |
|
62 |
12
|
ad2antrr |
|
63 |
|
elrel |
|
64 |
62 63
|
sylan |
|
65 |
|
breq1 |
|
66 |
65
|
notbid |
|
67 |
|
simplrr |
|
68 |
|
vex |
|
69 |
58 68
|
elimasn |
|
70 |
69
|
biimpri |
|
71 |
70
|
adantl |
|
72 |
66 67 71
|
rspcdva |
|
73 |
72
|
intnanrd |
|
74 |
|
opeq1 |
|
75 |
74
|
eleq1d |
|
76 |
75
|
anbi2d |
|
77 |
|
3anass |
|
78 |
|
olc |
|
79 |
78
|
biantrurd |
|
80 |
|
neeq1 |
|
81 |
80
|
orbi1d |
|
82 |
|
neirr |
|
83 |
|
biorf |
|
84 |
82 83
|
ax-mp |
|
85 |
81 84
|
bitr4di |
|
86 |
85
|
anbi2d |
|
87 |
|
andir |
|
88 |
|
nonconne |
|
89 |
88
|
biorfi |
|
90 |
87 89
|
bitr4i |
|
91 |
86 90
|
bitrdi |
|
92 |
79 91
|
bitr3d |
|
93 |
77 92
|
syl5bb |
|
94 |
93
|
notbid |
|
95 |
76 94
|
imbi12d |
|
96 |
73 95
|
mpbiri |
|
97 |
96
|
impcom |
|
98 |
|
breq1 |
|
99 |
98
|
notbid |
|
100 |
|
simplrr |
|
101 |
100
|
ad2antrr |
|
102 |
|
vex |
|
103 |
102 68
|
opeldm |
|
104 |
103
|
adantl |
|
105 |
104
|
adantr |
|
106 |
99 101 105
|
rspcdva |
|
107 |
|
simpr |
|
108 |
107
|
neneqd |
|
109 |
|
ioran |
|
110 |
106 108 109
|
sylanbrc |
|
111 |
110
|
intn3an1d |
|
112 |
97 111
|
pm2.61dane |
|
113 |
112
|
intn3an3d |
|
114 |
|
eleq1 |
|
115 |
114
|
anbi2d |
|
116 |
|
breq1 |
|
117 |
1
|
xpord2lem |
|
118 |
116 117
|
bitrdi |
|
119 |
118
|
notbid |
|
120 |
115 119
|
imbi12d |
|
121 |
113 120
|
mpbiri |
|
122 |
121
|
com12 |
|
123 |
122
|
exlimdvv |
|
124 |
64 123
|
mpd |
|
125 |
124
|
ralrimiva |
|
126 |
|
breq2 |
|
127 |
126
|
notbid |
|
128 |
127
|
ralbidv |
|
129 |
128
|
rspcev |
|
130 |
61 125 129
|
syl2anc |
|
131 |
56 130
|
rexlimddv |
|
132 |
30 131
|
rexlimddv |
|
133 |
132
|
ex |
|
134 |
133
|
alrimiv |
|
135 |
|
df-fr |
|
136 |
134 135
|
sylibr |
|