Step |
Hyp |
Ref |
Expression |
1 |
|
dynkin.p |
|
2 |
|
dynkin.l |
|
3 |
1
|
sigapisys |
|
4 |
2
|
sigaldsys |
|
5 |
3 4
|
ssini |
|
6 |
|
id |
|
7 |
6
|
elin1d |
|
8 |
1
|
ispisys |
|
9 |
7 8
|
sylib |
|
10 |
9
|
simpld |
|
11 |
10
|
elpwid |
|
12 |
|
dif0 |
|
13 |
6
|
elin2d |
|
14 |
2
|
isldsys |
|
15 |
13 14
|
sylib |
|
16 |
15
|
simprd |
|
17 |
16
|
simp2d |
|
18 |
16
|
simp1d |
|
19 |
|
difeq2 |
|
20 |
|
eqidd |
|
21 |
19 20
|
eleq12d |
|
22 |
21
|
rspcv |
|
23 |
18 22
|
syl |
|
24 |
17 23
|
mpd |
|
25 |
12 24
|
eqeltrrid |
|
26 |
|
unieq |
|
27 |
|
uni0 |
|
28 |
26 27
|
eqtrdi |
|
29 |
28
|
adantl |
|
30 |
18
|
ad3antrrr |
|
31 |
29 30
|
eqeltrd |
|
32 |
|
vex |
|
33 |
32
|
0sdom |
|
34 |
33
|
biimpri |
|
35 |
34
|
adantl |
|
36 |
|
simplr |
|
37 |
|
nnenom |
|
38 |
37
|
ensymi |
|
39 |
|
domentr |
|
40 |
36 38 39
|
sylancl |
|
41 |
|
fodomr |
|
42 |
35 40 41
|
syl2anc |
|
43 |
|
fveq2 |
|
44 |
43
|
iundisj |
|
45 |
|
fofn |
|
46 |
|
fniunfv |
|
47 |
45 46
|
syl |
|
48 |
|
forn |
|
49 |
48
|
unieqd |
|
50 |
47 49
|
eqtrd |
|
51 |
44 50
|
syl5eqr |
|
52 |
51
|
adantl |
|
53 |
|
fvex |
|
54 |
|
difexg |
|
55 |
53 54
|
ax-mp |
|
56 |
55
|
dfiun3 |
|
57 |
|
nfv |
|
58 |
|
nfcv |
|
59 |
|
nfmpt1 |
|
60 |
59
|
nfrn |
|
61 |
58 60
|
nfel |
|
62 |
57 61
|
nfan |
|
63 |
|
simpr |
|
64 |
|
nfv |
|
65 |
|
nfcv |
|
66 |
|
nfcv |
|
67 |
|
nfcv |
|
68 |
|
nfiu1 |
|
69 |
67 68
|
nfdif |
|
70 |
66 69
|
nfmpt |
|
71 |
70
|
nfrn |
|
72 |
65 71
|
nfel |
|
73 |
64 72
|
nfan |
|
74 |
|
nfv |
|
75 |
73 74
|
nfan |
|
76 |
65 69
|
nfeq |
|
77 |
75 76
|
nfan |
|
78 |
6
|
ad7antr |
|
79 |
|
simp-4r |
|
80 |
79
|
ad3antrrr |
|
81 |
80
|
elpwid |
|
82 |
|
fof |
|
83 |
82
|
ad4antlr |
|
84 |
|
simplr |
|
85 |
83 84
|
ffvelrnd |
|
86 |
81 85
|
sseldd |
|
87 |
|
fzofi |
|
88 |
87
|
a1i |
|
89 |
81
|
adantr |
|
90 |
83
|
adantr |
|
91 |
|
fzossnn |
|
92 |
91
|
a1i |
|
93 |
92
|
sselda |
|
94 |
90 93
|
ffvelrnd |
|
95 |
89 94
|
sseldd |
|
96 |
1 2 77 78 86 88 95
|
sigapildsyslem |
|
97 |
63 96
|
eqeltrd |
|
98 |
|
simpr |
|
99 |
|
eqid |
|
100 |
99 55
|
elrnmpti |
|
101 |
98 100
|
sylib |
|
102 |
62 97 101
|
r19.29af |
|
103 |
102
|
ex |
|
104 |
103
|
ssrdv |
|
105 |
|
nnex |
|
106 |
105
|
mptex |
|
107 |
106
|
rnex |
|
108 |
|
elpwg |
|
109 |
107 108
|
ax-mp |
|
110 |
104 109
|
sylibr |
|
111 |
16
|
simp3d |
|
112 |
111
|
ad4antr |
|
113 |
|
nnct |
|
114 |
|
mptct |
|
115 |
113 114
|
ax-mp |
|
116 |
|
rnct |
|
117 |
115 116
|
mp1i |
|
118 |
43
|
iundisj2 |
|
119 |
|
disjrnmpt |
|
120 |
118 119
|
mp1i |
|
121 |
|
breq1 |
|
122 |
|
disjeq1 |
|
123 |
121 122
|
anbi12d |
|
124 |
|
unieq |
|
125 |
124
|
eleq1d |
|
126 |
123 125
|
imbi12d |
|
127 |
126
|
rspcv |
|
128 |
127
|
imp |
|
129 |
128
|
imp |
|
130 |
110 112 117 120 129
|
syl22anc |
|
131 |
56 130
|
eqeltrid |
|
132 |
52 131
|
eqeltrrd |
|
133 |
42 132
|
exlimddv |
|
134 |
31 133
|
pm2.61dane |
|
135 |
134
|
ex |
|
136 |
135
|
ralrimiva |
|
137 |
25 17 136
|
3jca |
|
138 |
11 137
|
jca |
|
139 |
|
vex |
|
140 |
|
issiga |
|
141 |
139 140
|
ax-mp |
|
142 |
138 141
|
sylibr |
|
143 |
142
|
ssriv |
|
144 |
5 143
|
eqssi |
|