Step |
Hyp |
Ref |
Expression |
1 |
|
mretopd.m |
|
2 |
|
mretopd.z |
|
3 |
|
mretopd.u |
|
4 |
|
mretopd.j |
|
5 |
|
unieq |
|
6 |
|
uni0 |
|
7 |
5 6
|
eqtrdi |
|
8 |
7
|
eleq1d |
|
9 |
4
|
ssrab3 |
|
10 |
|
sstr |
|
11 |
9 10
|
mpan2 |
|
12 |
11
|
adantl |
|
13 |
|
sspwuni |
|
14 |
12 13
|
sylib |
|
15 |
|
vuniex |
|
16 |
15
|
elpw |
|
17 |
14 16
|
sylibr |
|
18 |
17
|
adantr |
|
19 |
|
uniiun |
|
20 |
19
|
difeq2i |
|
21 |
|
iindif2 |
|
22 |
21
|
adantl |
|
23 |
1
|
ad2antrr |
|
24 |
|
simpr |
|
25 |
|
difeq2 |
|
26 |
25
|
eleq1d |
|
27 |
26 4
|
elrab2 |
|
28 |
27
|
simprbi |
|
29 |
28
|
rgen |
|
30 |
|
ssralv |
|
31 |
30
|
adantl |
|
32 |
29 31
|
mpi |
|
33 |
32
|
adantr |
|
34 |
|
mreiincl |
|
35 |
23 24 33 34
|
syl3anc |
|
36 |
22 35
|
eqeltrrd |
|
37 |
20 36
|
eqeltrid |
|
38 |
|
difeq2 |
|
39 |
38
|
eleq1d |
|
40 |
39 4
|
elrab2 |
|
41 |
18 37 40
|
sylanbrc |
|
42 |
|
0elpw |
|
43 |
42
|
a1i |
|
44 |
|
mre1cl |
|
45 |
1 44
|
syl |
|
46 |
|
difeq2 |
|
47 |
|
dif0 |
|
48 |
46 47
|
eqtrdi |
|
49 |
48
|
eleq1d |
|
50 |
49 4
|
elrab2 |
|
51 |
43 45 50
|
sylanbrc |
|
52 |
51
|
adantr |
|
53 |
8 41 52
|
pm2.61ne |
|
54 |
53
|
ex |
|
55 |
54
|
alrimiv |
|
56 |
|
inss1 |
|
57 |
|
difeq2 |
|
58 |
57
|
eleq1d |
|
59 |
58 4
|
elrab2 |
|
60 |
59
|
simplbi |
|
61 |
60
|
elpwid |
|
62 |
61
|
ad2antrl |
|
63 |
56 62
|
sstrid |
|
64 |
|
vex |
|
65 |
64
|
inex1 |
|
66 |
65
|
elpw |
|
67 |
63 66
|
sylibr |
|
68 |
|
difindi |
|
69 |
59
|
simprbi |
|
70 |
69
|
ad2antrl |
|
71 |
28
|
ad2antll |
|
72 |
|
simpl |
|
73 |
|
uneq1 |
|
74 |
73
|
eleq1d |
|
75 |
74
|
imbi2d |
|
76 |
|
uneq2 |
|
77 |
76
|
eleq1d |
|
78 |
77
|
imbi2d |
|
79 |
3
|
3expb |
|
80 |
79
|
expcom |
|
81 |
75 78 80
|
vtocl2ga |
|
82 |
81
|
imp |
|
83 |
70 71 72 82
|
syl21anc |
|
84 |
68 83
|
eqeltrid |
|
85 |
|
difeq2 |
|
86 |
85
|
eleq1d |
|
87 |
86 4
|
elrab2 |
|
88 |
67 84 87
|
sylanbrc |
|
89 |
88
|
ralrimivva |
|
90 |
45
|
pwexd |
|
91 |
4 90
|
rabexd |
|
92 |
|
istopg |
|
93 |
91 92
|
syl |
|
94 |
55 89 93
|
mpbir2and |
|
95 |
9
|
unissi |
|
96 |
|
unipw |
|
97 |
95 96
|
sseqtri |
|
98 |
|
pwidg |
|
99 |
45 98
|
syl |
|
100 |
|
difid |
|
101 |
100 2
|
eqeltrid |
|
102 |
|
difeq2 |
|
103 |
102
|
eleq1d |
|
104 |
103 4
|
elrab2 |
|
105 |
99 101 104
|
sylanbrc |
|
106 |
|
unissel |
|
107 |
97 105 106
|
sylancr |
|
108 |
107
|
eqcomd |
|
109 |
|
istopon |
|
110 |
94 108 109
|
sylanbrc |
|
111 |
|
eqid |
|
112 |
111
|
cldval |
|
113 |
94 112
|
syl |
|
114 |
107
|
pweqd |
|
115 |
107
|
difeq1d |
|
116 |
115
|
eleq1d |
|
117 |
114 116
|
rabeqbidv |
|
118 |
4
|
eleq2i |
|
119 |
|
difss |
|
120 |
|
elpw2g |
|
121 |
45 120
|
syl |
|
122 |
119 121
|
mpbiri |
|
123 |
|
difeq2 |
|
124 |
123
|
eleq1d |
|
125 |
124
|
elrab3 |
|
126 |
122 125
|
syl |
|
127 |
126
|
adantr |
|
128 |
118 127
|
syl5bb |
|
129 |
|
elpwi |
|
130 |
|
dfss4 |
|
131 |
129 130
|
sylib |
|
132 |
131
|
adantl |
|
133 |
132
|
eleq1d |
|
134 |
128 133
|
bitrd |
|
135 |
134
|
rabbidva |
|
136 |
|
incom |
|
137 |
|
dfin5 |
|
138 |
136 137
|
eqtri |
|
139 |
|
mresspw |
|
140 |
1 139
|
syl |
|
141 |
|
df-ss |
|
142 |
140 141
|
sylib |
|
143 |
138 142
|
syl5eqr |
|
144 |
135 143
|
eqtrd |
|
145 |
113 117 144
|
3eqtrrd |
|
146 |
110 145
|
jca |
|