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
|
relopabi |
|
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 |
16 17
|
syl |
|
19 |
|
f1ofo |
|
20 |
|
forn |
|
21 |
18 19 20
|
3syl |
|
22 |
1 2 3 4 5 6 7 8
|
fpwwe2lem7 |
|
23 |
22
|
rneqd |
|
24 |
21 23
|
eqtr3d |
|
25 |
|
df-ima |
|
26 |
24 25
|
eqtr4di |
|
27 |
|
imassrn |
|
28 |
9
|
brrelex1i |
|
29 |
5 28
|
syl |
|
30 |
1 2
|
fpwwe2lem2 |
|
31 |
5 30
|
mpbid |
|
32 |
31
|
simprld |
|
33 |
7
|
oiiso |
|
34 |
29 32 33
|
syl2anc |
|
35 |
|
isof1o |
|
36 |
34 35
|
syl |
|
37 |
|
f1ofo |
|
38 |
|
forn |
|
39 |
36 37 38
|
3syl |
|
40 |
27 39
|
sseqtrid |
|
41 |
26 40
|
eqsstrd |
|
42 |
13
|
simplrd |
|
43 |
|
relxp |
|
44 |
|
relss |
|
45 |
42 43 44
|
mpisyl |
|
46 |
|
relinxp |
|
47 |
45 46
|
jctir |
|
48 |
42
|
ssbrd |
|
49 |
|
brxp |
|
50 |
48 49
|
syl6ib |
|
51 |
|
brinxp2 |
|
52 |
|
isocnv |
|
53 |
34 52
|
syl |
|
54 |
53
|
adantr |
|
55 |
|
isof1o |
|
56 |
|
f1ofn |
|
57 |
54 55 56
|
3syl |
|
58 |
|
simprll |
|
59 |
|
simprr |
|
60 |
41
|
adantr |
|
61 |
|
simprlr |
|
62 |
60 61
|
sseldd |
|
63 |
|
isorel |
|
64 |
54 58 62 63
|
syl12anc |
|
65 |
59 64
|
mpbid |
|
66 |
|
fvex |
|
67 |
66
|
epeli |
|
68 |
65 67
|
sylib |
|
69 |
22
|
adantr |
|
70 |
69
|
cnveqd |
|
71 |
|
fnfun |
|
72 |
|
funcnvres |
|
73 |
57 71 72
|
3syl |
|
74 |
70 73
|
eqtrd |
|
75 |
74
|
fveq1d |
|
76 |
26
|
adantr |
|
77 |
61 76
|
eleqtrd |
|
78 |
77
|
fvresd |
|
79 |
75 78
|
eqtrd |
|
80 |
|
isocnv |
|
81 |
16 80
|
syl |
|
82 |
|
isof1o |
|
83 |
|
f1of |
|
84 |
81 82 83
|
3syl |
|
85 |
84
|
adantr |
|
86 |
85 61
|
ffvelrnd |
|
87 |
79 86
|
eqeltrrd |
|
88 |
6
|
oicl |
|
89 |
|
ordtr1 |
|
90 |
88 89
|
ax-mp |
|
91 |
68 87 90
|
syl2anc |
|
92 |
57 58 91
|
elpreimad |
|
93 |
|
imacnvcnv |
|
94 |
76 93
|
eqtr4di |
|
95 |
92 94
|
eleqtrrd |
|
96 |
95 61
|
jca |
|
97 |
96
|
ex |
|
98 |
51 97
|
syl5bi |
|
99 |
22
|
adantr |
|
100 |
99
|
cnveqd |
|
101 |
100
|
fveq1d |
|
102 |
100
|
fveq1d |
|
103 |
101 102
|
breq12d |
|
104 |
|
isorel |
|
105 |
81 104
|
sylan |
|
106 |
|
eqidd |
|
107 |
|
isores3 |
|
108 |
34 8 106 107
|
syl3anc |
|
109 |
|
isocnv |
|
110 |
108 109
|
syl |
|
111 |
110
|
adantr |
|
112 |
|
simprl |
|
113 |
26
|
adantr |
|
114 |
112 113
|
eleqtrd |
|
115 |
|
simprr |
|
116 |
115 113
|
eleqtrd |
|
117 |
|
isorel |
|
118 |
111 114 116 117
|
syl12anc |
|
119 |
103 105 118
|
3bitr4d |
|
120 |
41
|
sselda |
|
121 |
120
|
adantrr |
|
122 |
121 115
|
jca |
|
123 |
122
|
biantrurd |
|
124 |
123 51
|
bitr4di |
|
125 |
119 124
|
bitrd |
|
126 |
125
|
ex |
|
127 |
50 98 126
|
pm5.21ndd |
|
128 |
|
df-br |
|
129 |
|
df-br |
|
130 |
127 128 129
|
3bitr3g |
|
131 |
130
|
eqrelrdv2 |
|
132 |
47 131
|
mpancom |
|
133 |
41 132
|
jca |
|