Step |
Hyp |
Ref |
Expression |
1 |
|
fpwwe2.1 |
|
2 |
|
fpwwe2.2 |
|
3 |
|
fpwwe2.3 |
|
4 |
|
fpwwe2.4 |
|
5 |
1 2 3 4
|
fpwwe2lem10 |
|
6 |
5
|
ffund |
|
7 |
|
funbrfv2b |
|
8 |
6 7
|
syl |
|
9 |
8
|
simprbda |
|
10 |
9
|
adantrr |
|
11 |
|
elssuni |
|
12 |
11 4
|
sseqtrrdi |
|
13 |
10 12
|
syl |
|
14 |
|
simpl |
|
15 |
14
|
a1i |
|
16 |
|
simplrr |
|
17 |
2
|
adantr |
|
18 |
17
|
adantr |
|
19 |
1 2 3 4
|
fpwwe2lem11 |
|
20 |
|
funfvbrb |
|
21 |
6 20
|
syl |
|
22 |
19 21
|
mpbid |
|
23 |
1 2
|
fpwwe2lem2 |
|
24 |
22 23
|
mpbid |
|
25 |
24
|
ad2antrr |
|
26 |
25
|
simpld |
|
27 |
26
|
simpld |
|
28 |
18 27
|
ssexd |
|
29 |
|
difexg |
|
30 |
28 29
|
syl |
|
31 |
25
|
simprd |
|
32 |
31
|
simpld |
|
33 |
|
wefr |
|
34 |
32 33
|
syl |
|
35 |
|
difssd |
|
36 |
|
fri |
|
37 |
36
|
expr |
|
38 |
30 34 35 37
|
syl21anc |
|
39 |
|
ssdif0 |
|
40 |
|
indif1 |
|
41 |
40
|
eqeq1i |
|
42 |
|
disj |
|
43 |
|
vex |
|
44 |
43
|
eliniseg |
|
45 |
44
|
elv |
|
46 |
45
|
notbii |
|
47 |
46
|
ralbii |
|
48 |
42 47
|
bitri |
|
49 |
39 41 48
|
3bitr2i |
|
50 |
|
cnvimass |
|
51 |
26
|
simprd |
|
52 |
|
dmss |
|
53 |
51 52
|
syl |
|
54 |
|
dmxpid |
|
55 |
53 54
|
sseqtrdi |
|
56 |
50 55
|
sstrid |
|
57 |
|
sseqin2 |
|
58 |
56 57
|
sylib |
|
59 |
58
|
sseq1d |
|
60 |
49 59
|
bitr3id |
|
61 |
60
|
rexbidv |
|
62 |
|
eldifn |
|
63 |
62
|
ad2antrl |
|
64 |
|
eleq1w |
|
65 |
64
|
notbid |
|
66 |
63 65
|
syl5ibrcom |
|
67 |
66
|
con2d |
|
68 |
67
|
imp |
|
69 |
63
|
adantr |
|
70 |
|
simprr |
|
71 |
70
|
ad2antrr |
|
72 |
71
|
breqd |
|
73 |
|
eldifi |
|
74 |
73
|
ad2antrl |
|
75 |
74
|
adantr |
|
76 |
|
simpr |
|
77 |
|
brxp |
|
78 |
75 76 77
|
sylanbrc |
|
79 |
|
brin |
|
80 |
79
|
rbaib |
|
81 |
78 80
|
syl |
|
82 |
72 81
|
bitrd |
|
83 |
1 2
|
fpwwe2lem2 |
|
84 |
83
|
biimpa |
|
85 |
84
|
adantrr |
|
86 |
85
|
simpld |
|
87 |
86
|
simprd |
|
88 |
87
|
ad5ant12 |
|
89 |
88
|
ssbrd |
|
90 |
|
brxp |
|
91 |
90
|
simplbi |
|
92 |
89 91
|
syl6 |
|
93 |
82 92
|
sylbird |
|
94 |
69 93
|
mtod |
|
95 |
32
|
ad2antrr |
|
96 |
|
weso |
|
97 |
95 96
|
syl |
|
98 |
13
|
ad2antrr |
|
99 |
98
|
sselda |
|
100 |
|
sotric |
|
101 |
|
ioran |
|
102 |
100 101
|
bitrdi |
|
103 |
97 99 75 102
|
syl12anc |
|
104 |
68 94 103
|
mpbir2and |
|
105 |
104 45
|
sylibr |
|
106 |
105
|
ex |
|
107 |
106
|
ssrdv |
|
108 |
|
simprr |
|
109 |
107 108
|
eqssd |
|
110 |
|
in32 |
|
111 |
|
simplrr |
|
112 |
111
|
ineq1d |
|
113 |
87
|
ad2antrr |
|
114 |
|
df-ss |
|
115 |
113 114
|
sylib |
|
116 |
112 115
|
eqtr3d |
|
117 |
|
inss2 |
|
118 |
|
xpss1 |
|
119 |
98 118
|
syl |
|
120 |
117 119
|
sstrid |
|
121 |
|
df-ss |
|
122 |
120 121
|
sylib |
|
123 |
110 116 122
|
3eqtr3a |
|
124 |
109
|
sqxpeqd |
|
125 |
124
|
ineq2d |
|
126 |
123 125
|
eqtrd |
|
127 |
109 126
|
oveq12d |
|
128 |
18
|
adantr |
|
129 |
22
|
adantr |
|
130 |
129
|
ad2antrr |
|
131 |
1 128 130
|
fpwwe2lem3 |
|
132 |
74 131
|
mpdan |
|
133 |
127 132
|
eqtrd |
|
134 |
133 63
|
eqneltrd |
|
135 |
134
|
rexlimdvaa |
|
136 |
61 135
|
sylbid |
|
137 |
38 136
|
syld |
|
138 |
137
|
necon4ad |
|
139 |
16 138
|
mpd |
|
140 |
|
ssdif0 |
|
141 |
139 140
|
sylibr |
|
142 |
141
|
ex |
|
143 |
3
|
adantlr |
|
144 |
|
simprl |
|
145 |
1 17 143 129 144
|
fpwwe2lem9 |
|
146 |
15 142 145
|
mpjaod |
|
147 |
13 146
|
eqssd |
|
148 |
6
|
adantr |
|
149 |
147 144
|
eqbrtrrd |
|
150 |
|
funbrfv |
|
151 |
148 149 150
|
sylc |
|
152 |
151
|
eqcomd |
|
153 |
147 152
|
jca |
|
154 |
153
|
ex |
|
155 |
1 2 3 4
|
fpwwe2lem12 |
|
156 |
22 155
|
jca |
|
157 |
|
breq12 |
|
158 |
|
oveq12 |
|
159 |
|
simpl |
|
160 |
158 159
|
eleq12d |
|
161 |
157 160
|
anbi12d |
|
162 |
156 161
|
syl5ibrcom |
|
163 |
154 162
|
impbid |
|