Step |
Hyp |
Ref |
Expression |
1 |
|
ssmxidl.1 |
|
2 |
|
ssmxidllem.1 |
|
3 |
|
ssmxidllem.2 |
|
4 |
|
ssmxidllem.3 |
|
5 |
|
ssmxidllem.4 |
|
6 |
|
ssmxidllem2.1 |
|
7 |
|
ssmxidllem2.2 |
|
8 |
|
ssmxidllem2.3 |
|
9 |
|
neeq1 |
|
10 |
|
sseq2 |
|
11 |
9 10
|
anbi12d |
|
12 |
2
|
ssrab3 |
|
13 |
6 12
|
sstrdi |
|
14 |
13
|
sselda |
|
15 |
|
eqid |
|
16 |
1 15
|
lidlss |
|
17 |
14 16
|
syl |
|
18 |
17
|
ralrimiva |
|
19 |
|
unissb |
|
20 |
18 19
|
sylibr |
|
21 |
3
|
adantr |
|
22 |
|
eqid |
|
23 |
15 22
|
lidl0cl |
|
24 |
21 14 23
|
syl2anc |
|
25 |
|
n0i |
|
26 |
24 25
|
syl |
|
27 |
26
|
reximdva0 |
|
28 |
7 27
|
mpdan |
|
29 |
|
rexnal |
|
30 |
28 29
|
sylib |
|
31 |
|
uni0c |
|
32 |
31
|
necon3abii |
|
33 |
30 32
|
sylibr |
|
34 |
|
eluni2 |
|
35 |
|
eluni2 |
|
36 |
34 35
|
anbi12i |
|
37 |
|
an32 |
|
38 |
3
|
ad6antr |
|
39 |
13
|
ad5antr |
|
40 |
|
simp-4r |
|
41 |
39 40
|
sseldd |
|
42 |
41
|
adantr |
|
43 |
|
simp-6r |
|
44 |
|
simpr |
|
45 |
|
simplr |
|
46 |
44 45
|
sseldd |
|
47 |
|
eqid |
|
48 |
15 1 47
|
lidlmcl |
|
49 |
38 42 43 46 48
|
syl22anc |
|
50 |
|
simp-4r |
|
51 |
|
eqid |
|
52 |
15 51
|
lidlacl |
|
53 |
38 42 49 50 52
|
syl22anc |
|
54 |
40
|
adantr |
|
55 |
|
elunii |
|
56 |
53 54 55
|
syl2anc |
|
57 |
3
|
ad6antr |
|
58 |
39
|
adantr |
|
59 |
|
simplr |
|
60 |
59
|
adantr |
|
61 |
58 60
|
sseldd |
|
62 |
|
simp-6r |
|
63 |
|
simplr |
|
64 |
15 1 47
|
lidlmcl |
|
65 |
57 61 62 63 64
|
syl22anc |
|
66 |
|
simpr |
|
67 |
|
simp-4r |
|
68 |
66 67
|
sseldd |
|
69 |
15 51
|
lidlacl |
|
70 |
57 61 65 68 69
|
syl22anc |
|
71 |
|
elunii |
|
72 |
70 60 71
|
syl2anc |
|
73 |
8
|
ad5antr |
|
74 |
|
sorpssi |
|
75 |
73 59 40 74
|
syl12anc |
|
76 |
56 72 75
|
mpjaodan |
|
77 |
76
|
r19.29an |
|
78 |
77
|
an32s |
|
79 |
37 78
|
sylanb |
|
80 |
79
|
r19.29an |
|
81 |
80
|
anasss |
|
82 |
36 81
|
sylan2b |
|
83 |
82
|
ralrimivva |
|
84 |
83
|
ralrimiva |
|
85 |
15 1 51 47
|
islidl |
|
86 |
20 33 84 85
|
syl3anbrc |
|
87 |
6
|
sselda |
|
88 |
|
neeq1 |
|
89 |
|
sseq2 |
|
90 |
88 89
|
anbi12d |
|
91 |
90 2
|
elrab2 |
|
92 |
87 91
|
sylib |
|
93 |
92
|
simprld |
|
94 |
|
eqid |
|
95 |
1 94
|
pridln1 |
|
96 |
21 14 93 95
|
syl3anc |
|
97 |
96
|
nrexdv |
|
98 |
|
eluni2 |
|
99 |
97 98
|
sylnibr |
|
100 |
15 1 94
|
lidl1el |
|
101 |
3 86 100
|
syl2anc |
|
102 |
101
|
necon3bbid |
|
103 |
99 102
|
mpbid |
|
104 |
92
|
simprrd |
|
105 |
104
|
ralrimiva |
|
106 |
|
ssint |
|
107 |
105 106
|
sylibr |
|
108 |
|
intssuni |
|
109 |
7 108
|
syl |
|
110 |
107 109
|
sstrd |
|
111 |
103 110
|
jca |
|
112 |
11 86 111
|
elrabd |
|
113 |
112 2
|
eleqtrrdi |
|