Step |
Hyp |
Ref |
Expression |
1 |
|
meadjiunlem.f |
|
2 |
|
meadjiunlem.3 |
|
3 |
|
meadjiunlem.x |
|
4 |
|
meadjiunlem.g |
|
5 |
|
meadjiunlem.y |
|
6 |
|
meadjiunlem.dj |
|
7 |
|
nfv |
|
8 |
4 3
|
jca |
|
9 |
|
fex |
|
10 |
|
rnexg |
|
11 |
8 9 10
|
3syl |
|
12 |
|
difssd |
|
13 |
1 2
|
meaf |
|
14 |
13
|
adantr |
|
15 |
4
|
frnd |
|
16 |
15
|
adantr |
|
17 |
12
|
sselda |
|
18 |
16 17
|
sseldd |
|
19 |
14 18
|
ffvelrnd |
|
20 |
|
simpl |
|
21 |
|
id |
|
22 |
|
dfin4 |
|
23 |
22
|
eqcomi |
|
24 |
21 23
|
eleqtrdi |
|
25 |
|
elinel2 |
|
26 |
|
elsni |
|
27 |
25 26
|
syl |
|
28 |
24 27
|
syl |
|
29 |
28
|
adantl |
|
30 |
|
simpr |
|
31 |
30
|
fveq2d |
|
32 |
1
|
mea0 |
|
33 |
32
|
adantr |
|
34 |
31 33
|
eqtrd |
|
35 |
20 29 34
|
syl2anc |
|
36 |
7 11 12 19 35
|
sge0ss |
|
37 |
36
|
eqcomd |
|
38 |
13 15
|
feqresmpt |
|
39 |
38
|
fveq2d |
|
40 |
4
|
ffvelrnda |
|
41 |
4
|
feqmptd |
|
42 |
13
|
feqmptd |
|
43 |
|
fveq2 |
|
44 |
40 41 42 43
|
fmptco |
|
45 |
44
|
fveq2d |
|
46 |
|
nfv |
|
47 |
|
ssrab2 |
|
48 |
47
|
a1i |
|
49 |
5 48
|
eqsstrid |
|
50 |
13
|
adantr |
|
51 |
4
|
adantr |
|
52 |
49
|
sselda |
|
53 |
51 52
|
ffvelrnd |
|
54 |
50 53
|
ffvelrnd |
|
55 |
|
eldifi |
|
56 |
55
|
ad2antlr |
|
57 |
|
fveq2 |
|
58 |
57
|
adantl |
|
59 |
1
|
adantr |
|
60 |
59
|
mea0 |
|
61 |
58 60
|
eqtrd |
|
62 |
61
|
ad4ant14 |
|
63 |
|
neneq |
|
64 |
63
|
ad2antlr |
|
65 |
62 64
|
pm2.65da |
|
66 |
65
|
neqned |
|
67 |
56 66
|
jca |
|
68 |
|
fveq2 |
|
69 |
68
|
neeq1d |
|
70 |
69
|
elrab |
|
71 |
67 70
|
sylibr |
|
72 |
71 5
|
eleqtrrdi |
|
73 |
|
eldifn |
|
74 |
73
|
ad2antlr |
|
75 |
72 74
|
pm2.65da |
|
76 |
|
nne |
|
77 |
75 76
|
sylib |
|
78 |
46 3 49 54 77
|
sge0ss |
|
79 |
78
|
eqcomd |
|
80 |
3 49
|
ssexd |
|
81 |
|
nfv |
|
82 |
|
eqid |
|
83 |
4
|
ffnd |
|
84 |
|
dffn3 |
|
85 |
83 84
|
sylib |
|
86 |
85
|
adantr |
|
87 |
49
|
sselda |
|
88 |
86 87
|
ffvelrnd |
|
89 |
5
|
eleq2i |
|
90 |
|
rabid |
|
91 |
89 90
|
bitri |
|
92 |
91
|
biimpi |
|
93 |
92
|
simprd |
|
94 |
93
|
adantl |
|
95 |
|
nelsn |
|
96 |
94 95
|
syl |
|
97 |
88 96
|
eldifd |
|
98 |
|
disjss1 |
|
99 |
49 6 98
|
sylc |
|
100 |
81 82 97 94 99
|
disjf1 |
|
101 |
4 49
|
feqresmpt |
|
102 |
|
f1eq1 |
|
103 |
101 102
|
syl |
|
104 |
100 103
|
mpbird |
|
105 |
101
|
rneqd |
|
106 |
97
|
ralrimiva |
|
107 |
82
|
rnmptss |
|
108 |
106 107
|
syl |
|
109 |
105 108
|
eqsstrd |
|
110 |
|
simpl |
|
111 |
|
eldifi |
|
112 |
111
|
adantl |
|
113 |
|
eldifsni |
|
114 |
113
|
adantl |
|
115 |
|
simpr |
|
116 |
|
fvelrnb |
|
117 |
83 116
|
syl |
|
118 |
117
|
adantr |
|
119 |
115 118
|
mpbid |
|
120 |
119
|
3adant3 |
|
121 |
|
id |
|
122 |
121
|
eqcomd |
|
123 |
122
|
3ad2ant3 |
|
124 |
|
simp1l |
|
125 |
|
simp2 |
|
126 |
|
simpr |
|
127 |
|
simpl |
|
128 |
126 127
|
eqnetrd |
|
129 |
128
|
adantll |
|
130 |
129
|
3adant2 |
|
131 |
91
|
biimpri |
|
132 |
|
fvexd |
|
133 |
82
|
elrnmpt1 |
|
134 |
131 132 133
|
syl2anc |
|
135 |
134
|
3adant1 |
|
136 |
105
|
eqcomd |
|
137 |
136
|
3ad2ant1 |
|
138 |
135 137
|
eleqtrd |
|
139 |
124 125 130 138
|
syl3anc |
|
140 |
123 139
|
eqeltrd |
|
141 |
140
|
3exp |
|
142 |
141
|
rexlimdv |
|
143 |
142
|
3adant2 |
|
144 |
120 143
|
mpd |
|
145 |
110 112 114 144
|
syl3anc |
|
146 |
109 145
|
eqelssd |
|
147 |
104 146
|
jca |
|
148 |
|
dff1o5 |
|
149 |
147 148
|
sylibr |
|
150 |
|
fvres |
|
151 |
150
|
adantl |
|
152 |
7 46 43 80 149 151 19
|
sge0f1o |
|
153 |
152
|
eqcomd |
|
154 |
45 79 153
|
3eqtrd |
|
155 |
37 39 154
|
3eqtr4d |
|