Step |
Hyp |
Ref |
Expression |
1 |
|
neitr.1 |
|
2 |
|
nfv |
|
3 |
|
nfv |
|
4 |
|
nfre1 |
|
5 |
3 4
|
nfan |
|
6 |
2 5
|
nfan |
|
7 |
|
simpl |
|
8 |
7
|
anim2i |
|
9 |
|
simp-5r |
|
10 |
|
simp1 |
|
11 |
|
simp2 |
|
12 |
1
|
restuni |
|
13 |
10 11 12
|
syl2anc |
|
14 |
13
|
ad5antr |
|
15 |
9 14
|
sseqtrrd |
|
16 |
11
|
ad5antr |
|
17 |
15 16
|
sstrd |
|
18 |
10
|
ad5antr |
|
19 |
|
simplr |
|
20 |
1
|
eltopss |
|
21 |
18 19 20
|
syl2anc |
|
22 |
21
|
ssdifssd |
|
23 |
17 22
|
unssd |
|
24 |
|
simpr1l |
|
25 |
24
|
3anassrs |
|
26 |
|
simpr |
|
27 |
25 26
|
sseqtrd |
|
28 |
|
inss1 |
|
29 |
27 28
|
sstrdi |
|
30 |
|
inundif |
|
31 |
|
simpr1r |
|
32 |
31
|
3anassrs |
|
33 |
26 32
|
eqsstrrd |
|
34 |
|
unss1 |
|
35 |
33 34
|
syl |
|
36 |
30 35
|
eqsstrrid |
|
37 |
|
sseq2 |
|
38 |
|
sseq1 |
|
39 |
37 38
|
anbi12d |
|
40 |
39
|
rspcev |
|
41 |
19 29 36 40
|
syl12anc |
|
42 |
|
indir |
|
43 |
|
incom |
|
44 |
|
disjdif |
|
45 |
43 44
|
eqtr3i |
|
46 |
45
|
uneq2i |
|
47 |
|
un0 |
|
48 |
42 46 47
|
3eqtri |
|
49 |
|
df-ss |
|
50 |
49
|
biimpi |
|
51 |
48 50
|
syl5req |
|
52 |
15 51
|
syl |
|
53 |
|
vex |
|
54 |
|
vex |
|
55 |
54
|
difexi |
|
56 |
53 55
|
unex |
|
57 |
|
sseq1 |
|
58 |
|
sseq2 |
|
59 |
58
|
anbi2d |
|
60 |
59
|
rexbidv |
|
61 |
57 60
|
anbi12d |
|
62 |
|
ineq1 |
|
63 |
62
|
eqeq2d |
|
64 |
61 63
|
anbi12d |
|
65 |
56 64
|
spcev |
|
66 |
23 41 52 65
|
syl21anc |
|
67 |
10
|
ad3antrrr |
|
68 |
10
|
uniexd |
|
69 |
1 68
|
eqeltrid |
|
70 |
69 11
|
ssexd |
|
71 |
70
|
ad3antrrr |
|
72 |
|
simplr |
|
73 |
|
elrest |
|
74 |
73
|
biimpa |
|
75 |
67 71 72 74
|
syl21anc |
|
76 |
66 75
|
r19.29a |
|
77 |
8 76
|
sylanl1 |
|
78 |
|
simprr |
|
79 |
6 77 78
|
r19.29af |
|
80 |
|
inss2 |
|
81 |
|
sseq1 |
|
82 |
80 81
|
mpbiri |
|
83 |
82
|
adantl |
|
84 |
83
|
exlimiv |
|
85 |
84
|
adantl |
|
86 |
13
|
adantr |
|
87 |
85 86
|
sseqtrd |
|
88 |
10
|
ad4antr |
|
89 |
70
|
ad4antr |
|
90 |
|
simplr |
|
91 |
|
elrestr |
|
92 |
88 89 90 91
|
syl3anc |
|
93 |
|
simprl |
|
94 |
|
simp3 |
|
95 |
94
|
ad4antr |
|
96 |
93 95
|
ssind |
|
97 |
|
simprr |
|
98 |
97
|
ssrind |
|
99 |
|
simp-4r |
|
100 |
98 99
|
sseqtrrd |
|
101 |
92 96 100
|
jca32 |
|
102 |
101
|
ex |
|
103 |
102
|
reximdva |
|
104 |
103
|
impr |
|
105 |
104
|
an32s |
|
106 |
105
|
expl |
|
107 |
106
|
exlimdv |
|
108 |
107
|
imp |
|
109 |
|
sseq2 |
|
110 |
|
sseq1 |
|
111 |
109 110
|
anbi12d |
|
112 |
111
|
rspcev |
|
113 |
112
|
rexlimivw |
|
114 |
108 113
|
syl |
|
115 |
87 114
|
jca |
|
116 |
79 115
|
impbida |
|
117 |
|
resttop |
|
118 |
10 70 117
|
syl2anc |
|
119 |
94 13
|
sseqtrd |
|
120 |
|
eqid |
|
121 |
120
|
isnei |
|
122 |
118 119 121
|
syl2anc |
|
123 |
|
fvex |
|
124 |
|
restval |
|
125 |
123 70 124
|
sylancr |
|
126 |
125
|
eleq2d |
|
127 |
94 11
|
sstrd |
|
128 |
|
eqid |
|
129 |
128
|
elrnmpt |
|
130 |
129
|
elv |
|
131 |
|
df-rex |
|
132 |
130 131
|
bitri |
|
133 |
1
|
isnei |
|
134 |
133
|
anbi1d |
|
135 |
134
|
exbidv |
|
136 |
132 135
|
syl5bb |
|
137 |
10 127 136
|
syl2anc |
|
138 |
126 137
|
bitrd |
|
139 |
116 122 138
|
3bitr4d |
|
140 |
139
|
eqrdv |
|