Step |
Hyp |
Ref |
Expression |
1 |
|
mbfsup.1 |
|
2 |
|
mbfsup.2 |
|
3 |
|
mbfsup.3 |
|
4 |
|
mbfsup.4 |
|
5 |
|
mbfsup.5 |
|
6 |
|
mbfsup.6 |
|
7 |
5
|
anassrs |
|
8 |
7
|
an32s |
|
9 |
8
|
fmpttd |
|
10 |
9
|
frnd |
|
11 |
|
uzid |
|
12 |
3 11
|
syl |
|
13 |
12 1
|
eleqtrrdi |
|
14 |
13
|
adantr |
|
15 |
|
eqid |
|
16 |
15 8
|
dmmptd |
|
17 |
14 16
|
eleqtrrd |
|
18 |
17
|
ne0d |
|
19 |
|
dm0rn0 |
|
20 |
19
|
necon3bii |
|
21 |
18 20
|
sylib |
|
22 |
9
|
ffnd |
|
23 |
|
breq1 |
|
24 |
23
|
ralrn |
|
25 |
22 24
|
syl |
|
26 |
|
nffvmpt1 |
|
27 |
|
nfcv |
|
28 |
|
nfcv |
|
29 |
26 27 28
|
nfbr |
|
30 |
|
nfv |
|
31 |
|
fveq2 |
|
32 |
31
|
breq1d |
|
33 |
29 30 32
|
cbvralw |
|
34 |
|
simpr |
|
35 |
15
|
fvmpt2 |
|
36 |
34 8 35
|
syl2anc |
|
37 |
36
|
breq1d |
|
38 |
37
|
ralbidva |
|
39 |
33 38
|
syl5bb |
|
40 |
25 39
|
bitrd |
|
41 |
40
|
rexbidv |
|
42 |
6 41
|
mpbird |
|
43 |
10 21 42
|
suprcld |
|
44 |
43 2
|
fmptd |
|
45 |
|
simpr |
|
46 |
|
ltso |
|
47 |
46
|
supex |
|
48 |
2
|
fvmpt2 |
|
49 |
45 47 48
|
sylancl |
|
50 |
49
|
breq2d |
|
51 |
10 21 42
|
3jca |
|
52 |
51
|
adantlr |
|
53 |
|
simplr |
|
54 |
|
suprlub |
|
55 |
52 53 54
|
syl2anc |
|
56 |
22
|
adantlr |
|
57 |
|
breq2 |
|
58 |
57
|
rexrn |
|
59 |
56 58
|
syl |
|
60 |
|
nfcv |
|
61 |
|
nfcv |
|
62 |
60 61 26
|
nfbr |
|
63 |
|
nfv |
|
64 |
31
|
breq2d |
|
65 |
62 63 64
|
cbvrexw |
|
66 |
15
|
fvmpt2i |
|
67 |
|
eqid |
|
68 |
67
|
fvmpt2i |
|
69 |
68
|
adantl |
|
70 |
69
|
eqcomd |
|
71 |
66 70
|
sylan9eqr |
|
72 |
71
|
breq2d |
|
73 |
72
|
rexbidva |
|
74 |
73
|
adantlr |
|
75 |
65 74
|
syl5bb |
|
76 |
59 75
|
bitrd |
|
77 |
50 55 76
|
3bitrd |
|
78 |
77
|
ralrimiva |
|
79 |
|
nfv |
|
80 |
|
nfcv |
|
81 |
|
nfcv |
|
82 |
|
nfmpt1 |
|
83 |
2 82
|
nfcxfr |
|
84 |
|
nfcv |
|
85 |
83 84
|
nffv |
|
86 |
80 81 85
|
nfbr |
|
87 |
|
nfcv |
|
88 |
|
nffvmpt1 |
|
89 |
80 81 88
|
nfbr |
|
90 |
87 89
|
nfrex |
|
91 |
86 90
|
nfbi |
|
92 |
|
fveq2 |
|
93 |
92
|
breq2d |
|
94 |
|
fveq2 |
|
95 |
94
|
breq2d |
|
96 |
95
|
rexbidv |
|
97 |
93 96
|
bibi12d |
|
98 |
79 91 97
|
cbvralw |
|
99 |
78 98
|
sylib |
|
100 |
99
|
r19.21bi |
|
101 |
44
|
adantr |
|
102 |
101
|
ffvelrnda |
|
103 |
|
rexr |
|
104 |
103
|
ad2antlr |
|
105 |
|
elioopnf |
|
106 |
104 105
|
syl |
|
107 |
102 106
|
mpbirand |
|
108 |
104
|
adantr |
|
109 |
|
elioopnf |
|
110 |
108 109
|
syl |
|
111 |
7
|
fmpttd |
|
112 |
111
|
ffvelrnda |
|
113 |
112
|
biantrurd |
|
114 |
113
|
an32s |
|
115 |
114
|
adantllr |
|
116 |
110 115
|
bitr4d |
|
117 |
116
|
rexbidva |
|
118 |
100 107 117
|
3bitr4d |
|
119 |
118
|
pm5.32da |
|
120 |
44
|
ffnd |
|
121 |
120
|
adantr |
|
122 |
|
elpreima |
|
123 |
121 122
|
syl |
|
124 |
|
eliun |
|
125 |
111
|
ffnd |
|
126 |
|
elpreima |
|
127 |
125 126
|
syl |
|
128 |
127
|
rexbidva |
|
129 |
128
|
adantr |
|
130 |
|
r19.42v |
|
131 |
129 130
|
bitrdi |
|
132 |
124 131
|
syl5bb |
|
133 |
119 123 132
|
3bitr4d |
|
134 |
133
|
eqrdv |
|
135 |
|
zex |
|
136 |
|
uzssz |
|
137 |
|
ssdomg |
|
138 |
135 136 137
|
mp2 |
|
139 |
1 138
|
eqbrtri |
|
140 |
|
znnen |
|
141 |
|
domentr |
|
142 |
139 140 141
|
mp2an |
|
143 |
|
mbfima |
|
144 |
4 111 143
|
syl2anc |
|
145 |
144
|
ralrimiva |
|
146 |
145
|
adantr |
|
147 |
|
iunmbl2 |
|
148 |
142 146 147
|
sylancr |
|
149 |
134 148
|
eqeltrd |
|
150 |
44 149
|
ismbf3d |
|