Step |
Hyp |
Ref |
Expression |
1 |
|
fpwwe2.1 |
|
2 |
|
fpwwe2.2 |
|
3 |
|
fpwwe2.3 |
|
4 |
|
fpwwe2lem8.x |
|
5 |
|
fpwwe2lem8.y |
|
6 |
|
fpwwe2lem8.m |
|
7 |
|
fpwwe2lem8.n |
|
8 |
|
fpwwe2lem8.s |
|
9 |
1
|
relopabiv |
|
10 |
9
|
brrelex1i |
|
11 |
4 10
|
syl |
|
12 |
1 2
|
fpwwe2lem2 |
|
13 |
4 12
|
mpbid |
|
14 |
13
|
simprld |
|
15 |
6
|
oiiso |
|
16 |
11 14 15
|
syl2anc |
|
17 |
|
isof1o |
|
18 |
|
f1ofo |
|
19 |
|
forn |
|
20 |
16 17 18 19
|
4syl |
|
21 |
1 2 3 4 5 6 7 8
|
fpwwe2lem7 |
|
22 |
21
|
rneqd |
|
23 |
20 22
|
eqtr3d |
|
24 |
|
df-ima |
|
25 |
23 24
|
eqtr4di |
|
26 |
|
imassrn |
|
27 |
9
|
brrelex1i |
|
28 |
5 27
|
syl |
|
29 |
1 2
|
fpwwe2lem2 |
|
30 |
5 29
|
mpbid |
|
31 |
30
|
simprld |
|
32 |
7
|
oiiso |
|
33 |
28 31 32
|
syl2anc |
|
34 |
|
isof1o |
|
35 |
|
f1ofo |
|
36 |
|
forn |
|
37 |
33 34 35 36
|
4syl |
|
38 |
26 37
|
sseqtrid |
|
39 |
25 38
|
eqsstrd |
|
40 |
13
|
simplrd |
|
41 |
|
relxp |
|
42 |
|
relss |
|
43 |
40 41 42
|
mpisyl |
|
44 |
|
relinxp |
|
45 |
43 44
|
jctir |
|
46 |
40
|
ssbrd |
|
47 |
|
brxp |
|
48 |
46 47
|
imbitrdi |
|
49 |
|
brinxp2 |
|
50 |
|
isocnv |
|
51 |
33 50
|
syl |
|
52 |
51
|
adantr |
|
53 |
|
isof1o |
|
54 |
|
f1ofn |
|
55 |
52 53 54
|
3syl |
|
56 |
|
simprll |
|
57 |
|
simprr |
|
58 |
39
|
adantr |
|
59 |
|
simprlr |
|
60 |
58 59
|
sseldd |
|
61 |
|
isorel |
|
62 |
52 56 60 61
|
syl12anc |
|
63 |
57 62
|
mpbid |
|
64 |
|
fvex |
|
65 |
64
|
epeli |
|
66 |
63 65
|
sylib |
|
67 |
21
|
adantr |
|
68 |
67
|
cnveqd |
|
69 |
|
fnfun |
|
70 |
|
funcnvres |
|
71 |
55 69 70
|
3syl |
|
72 |
68 71
|
eqtrd |
|
73 |
72
|
fveq1d |
|
74 |
25
|
adantr |
|
75 |
59 74
|
eleqtrd |
|
76 |
75
|
fvresd |
|
77 |
73 76
|
eqtrd |
|
78 |
|
isocnv |
|
79 |
|
isof1o |
|
80 |
|
f1of |
|
81 |
16 78 79 80
|
4syl |
|
82 |
81
|
adantr |
|
83 |
82 59
|
ffvelcdmd |
|
84 |
77 83
|
eqeltrrd |
|
85 |
6
|
oicl |
|
86 |
|
ordtr1 |
|
87 |
85 86
|
ax-mp |
|
88 |
66 84 87
|
syl2anc |
|
89 |
55 56 88
|
elpreimad |
|
90 |
|
imacnvcnv |
|
91 |
74 90
|
eqtr4di |
|
92 |
89 91
|
eleqtrrd |
|
93 |
92 59
|
jca |
|
94 |
93
|
ex |
|
95 |
49 94
|
biimtrid |
|
96 |
21
|
adantr |
|
97 |
96
|
cnveqd |
|
98 |
97
|
fveq1d |
|
99 |
97
|
fveq1d |
|
100 |
98 99
|
breq12d |
|
101 |
16 78
|
syl |
|
102 |
|
isorel |
|
103 |
101 102
|
sylan |
|
104 |
|
eqidd |
|
105 |
|
isores3 |
|
106 |
33 8 104 105
|
syl3anc |
|
107 |
|
isocnv |
|
108 |
106 107
|
syl |
|
109 |
108
|
adantr |
|
110 |
|
simprl |
|
111 |
25
|
adantr |
|
112 |
110 111
|
eleqtrd |
|
113 |
|
simprr |
|
114 |
113 111
|
eleqtrd |
|
115 |
|
isorel |
|
116 |
109 112 114 115
|
syl12anc |
|
117 |
100 103 116
|
3bitr4d |
|
118 |
39
|
sselda |
|
119 |
118
|
adantrr |
|
120 |
119 113
|
jca |
|
121 |
120
|
biantrurd |
|
122 |
121 49
|
bitr4di |
|
123 |
117 122
|
bitrd |
|
124 |
123
|
ex |
|
125 |
48 95 124
|
pm5.21ndd |
|
126 |
|
df-br |
|
127 |
|
df-br |
|
128 |
125 126 127
|
3bitr3g |
|
129 |
128
|
eqrelrdv2 |
|
130 |
45 129
|
mpancom |
|
131 |
39 130
|
jca |
|