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 |
|
fpwwe2lem5.1 |
|
9 |
|
fpwwe2lem5.2 |
|
10 |
|
fpwwe2lem5.3 |
|
11 |
1 2
|
fpwwe2lem2 |
|
12 |
4 11
|
mpbid |
|
13 |
12
|
simplrd |
|
14 |
13
|
ssbrd |
|
15 |
|
brxp |
|
16 |
15
|
simplbi |
|
17 |
14 16
|
syl6 |
|
18 |
17
|
imp |
|
19 |
|
imassrn |
|
20 |
1
|
relopabi |
|
21 |
20
|
brrelex1i |
|
22 |
5 21
|
syl |
|
23 |
1 2
|
fpwwe2lem2 |
|
24 |
5 23
|
mpbid |
|
25 |
24
|
simprld |
|
26 |
7
|
oiiso |
|
27 |
22 25 26
|
syl2anc |
|
28 |
27
|
adantr |
|
29 |
|
isof1o |
|
30 |
28 29
|
syl |
|
31 |
|
f1ofo |
|
32 |
|
forn |
|
33 |
30 31 32
|
3syl |
|
34 |
19 33
|
sseqtrid |
|
35 |
20
|
brrelex1i |
|
36 |
4 35
|
syl |
|
37 |
12
|
simprld |
|
38 |
6
|
oiiso |
|
39 |
36 37 38
|
syl2anc |
|
40 |
39
|
adantr |
|
41 |
|
isof1o |
|
42 |
40 41
|
syl |
|
43 |
|
f1ocnvfv2 |
|
44 |
42 18 43
|
syl2anc |
|
45 |
|
simpr |
|
46 |
44 45
|
eqbrtrd |
|
47 |
|
f1ocnv |
|
48 |
|
f1of |
|
49 |
42 47 48
|
3syl |
|
50 |
49 18
|
ffvelrnd |
|
51 |
8
|
adantr |
|
52 |
|
isorel |
|
53 |
40 50 51 52
|
syl12anc |
|
54 |
46 53
|
mpbird |
|
55 |
|
epelg |
|
56 |
51 55
|
syl |
|
57 |
54 56
|
mpbid |
|
58 |
|
ffn |
|
59 |
|
elpreima |
|
60 |
49 58 59
|
3syl |
|
61 |
18 57 60
|
mpbir2and |
|
62 |
|
imacnvcnv |
|
63 |
61 62
|
eleqtrdi |
|
64 |
10
|
adantr |
|
65 |
64
|
rneqd |
|
66 |
|
df-ima |
|
67 |
|
df-ima |
|
68 |
65 66 67
|
3eqtr4g |
|
69 |
63 68
|
eleqtrd |
|
70 |
34 69
|
sseldd |
|
71 |
64
|
cnveqd |
|
72 |
|
dff1o3 |
|
73 |
72
|
simprbi |
|
74 |
|
funcnvres |
|
75 |
42 73 74
|
3syl |
|
76 |
|
dff1o3 |
|
77 |
76
|
simprbi |
|
78 |
|
funcnvres |
|
79 |
30 77 78
|
3syl |
|
80 |
71 75 79
|
3eqtr3d |
|
81 |
80
|
fveq1d |
|
82 |
63
|
fvresd |
|
83 |
69
|
fvresd |
|
84 |
81 82 83
|
3eqtr3d |
|
85 |
18 70 84
|
3jca |
|