Step |
Hyp |
Ref |
Expression |
1 |
|
fnwe2.su |
|
2 |
|
fnwe2.t |
|
3 |
|
fnwe2.s |
|
4 |
|
fnwe2.f |
|
5 |
|
fnwe2.r |
|
6 |
|
fnwe2lem2.a |
|
7 |
|
fnwe2lem2.n0 |
|
8 |
|
ffun |
|
9 |
|
vex |
|
10 |
9
|
funimaex |
|
11 |
4 8 10
|
3syl |
|
12 |
|
wefr |
|
13 |
5 12
|
syl |
|
14 |
|
imassrn |
|
15 |
4
|
frnd |
|
16 |
14 15
|
sstrid |
|
17 |
|
incom |
|
18 |
4
|
fdmd |
|
19 |
6 18
|
sseqtrrd |
|
20 |
|
df-ss |
|
21 |
19 20
|
sylib |
|
22 |
17 21
|
syl5eq |
|
23 |
22 7
|
eqnetrd |
|
24 |
|
imadisj |
|
25 |
24
|
necon3bii |
|
26 |
23 25
|
sylibr |
|
27 |
|
fri |
|
28 |
11 13 16 26 27
|
syl22anc |
|
29 |
|
df-ima |
|
30 |
29
|
rexeqi |
|
31 |
4
|
ffnd |
|
32 |
|
fnssres |
|
33 |
31 6 32
|
syl2anc |
|
34 |
|
breq2 |
|
35 |
34
|
notbid |
|
36 |
35
|
ralbidv |
|
37 |
36
|
rexrn |
|
38 |
33 37
|
syl |
|
39 |
30 38
|
syl5bb |
|
40 |
29
|
raleqi |
|
41 |
|
breq1 |
|
42 |
41
|
notbid |
|
43 |
42
|
ralrn |
|
44 |
33 43
|
syl |
|
45 |
40 44
|
syl5bb |
|
46 |
45
|
adantr |
|
47 |
6
|
resabs1d |
|
48 |
47
|
ad2antrr |
|
49 |
48
|
fveq1d |
|
50 |
|
fvres |
|
51 |
50
|
adantl |
|
52 |
49 51
|
eqtrd |
|
53 |
48
|
fveq1d |
|
54 |
|
fvres |
|
55 |
54
|
ad2antlr |
|
56 |
53 55
|
eqtrd |
|
57 |
52 56
|
breq12d |
|
58 |
57
|
notbid |
|
59 |
58
|
ralbidva |
|
60 |
46 59
|
bitrd |
|
61 |
60
|
rexbidva |
|
62 |
39 61
|
bitrd |
|
63 |
9
|
inex1 |
|
64 |
63
|
a1i |
|
65 |
6
|
sselda |
|
66 |
1 2 3
|
fnwe2lem1 |
|
67 |
|
wefr |
|
68 |
66 67
|
syl |
|
69 |
65 68
|
syldan |
|
70 |
69
|
adantrr |
|
71 |
|
inss2 |
|
72 |
71
|
a1i |
|
73 |
|
simprl |
|
74 |
|
fveqeq2 |
|
75 |
65
|
adantrr |
|
76 |
|
eqidd |
|
77 |
74 75 76
|
elrabd |
|
78 |
73 77
|
elind |
|
79 |
78
|
ne0d |
|
80 |
|
fri |
|
81 |
64 70 72 79 80
|
syl22anc |
|
82 |
|
elin |
|
83 |
|
fveqeq2 |
|
84 |
83
|
elrab |
|
85 |
84
|
anbi2i |
|
86 |
82 85
|
bitri |
|
87 |
|
elin |
|
88 |
|
fveqeq2 |
|
89 |
88
|
elrab |
|
90 |
89
|
anbi2i |
|
91 |
87 90
|
bitri |
|
92 |
91
|
imbi1i |
|
93 |
|
impexp |
|
94 |
92 93
|
bitri |
|
95 |
94
|
ralbii2 |
|
96 |
|
simplrl |
|
97 |
|
fveq2 |
|
98 |
97
|
breq1d |
|
99 |
98
|
notbid |
|
100 |
|
simplrr |
|
101 |
100
|
ad2antrr |
|
102 |
|
simpr |
|
103 |
99 101 102
|
rspcdva |
|
104 |
|
simprrr |
|
105 |
104
|
ad2antrr |
|
106 |
105
|
breq2d |
|
107 |
103 106
|
mtbird |
|
108 |
6
|
ad3antrrr |
|
109 |
108
|
sselda |
|
110 |
109
|
adantrr |
|
111 |
|
simprr |
|
112 |
104
|
ad2antrr |
|
113 |
111 112
|
eqtrd |
|
114 |
|
eleq1w |
|
115 |
|
fveqeq2 |
|
116 |
114 115
|
anbi12d |
|
117 |
|
breq1 |
|
118 |
117
|
notbid |
|
119 |
116 118
|
imbi12d |
|
120 |
|
simplr |
|
121 |
|
simprl |
|
122 |
119 120 121
|
rspcdva |
|
123 |
110 113 122
|
mp2and |
|
124 |
111 112
|
eqtr2d |
|
125 |
124
|
csbeq1d |
|
126 |
125
|
breqd |
|
127 |
123 126
|
mtbid |
|
128 |
127
|
expr |
|
129 |
|
imnan |
|
130 |
128 129
|
sylib |
|
131 |
|
ioran |
|
132 |
107 130 131
|
sylanbrc |
|
133 |
1 2
|
fnwe2val |
|
134 |
132 133
|
sylnibr |
|
135 |
134
|
ralrimiva |
|
136 |
|
breq2 |
|
137 |
136
|
notbid |
|
138 |
137
|
ralbidv |
|
139 |
138
|
rspcev |
|
140 |
96 135 139
|
syl2anc |
|
141 |
140
|
ex |
|
142 |
95 141
|
syl5bi |
|
143 |
142
|
ex |
|
144 |
86 143
|
syl5bi |
|
145 |
144
|
rexlimdv |
|
146 |
81 145
|
mpd |
|
147 |
146
|
rexlimdvaa |
|
148 |
62 147
|
sylbid |
|
149 |
28 148
|
mpd |
|