Step |
Hyp |
Ref |
Expression |
1 |
|
imassrn |
|
2 |
|
isismty |
|
3 |
2
|
biimp3a |
|
4 |
3
|
adantr |
|
5 |
4
|
simpld |
|
6 |
|
f1of |
|
7 |
5 6
|
syl |
|
8 |
7
|
frnd |
|
9 |
1 8
|
sstrid |
|
10 |
9
|
sseld |
|
11 |
|
simpl2 |
|
12 |
|
simprl |
|
13 |
|
ffvelrn |
|
14 |
7 12 13
|
syl2anc |
|
15 |
|
simprr |
|
16 |
|
blssm |
|
17 |
11 14 15 16
|
syl3anc |
|
18 |
17
|
sseld |
|
19 |
|
simpl1 |
|
20 |
19
|
adantr |
|
21 |
|
simplrr |
|
22 |
|
simplrl |
|
23 |
|
f1ocnv |
|
24 |
|
f1of |
|
25 |
5 23 24
|
3syl |
|
26 |
|
ffvelrn |
|
27 |
25 26
|
sylan |
|
28 |
|
elbl2 |
|
29 |
20 21 22 27 28
|
syl22anc |
|
30 |
4
|
simprd |
|
31 |
|
oveq1 |
|
32 |
|
fveq2 |
|
33 |
32
|
oveq1d |
|
34 |
31 33
|
eqeq12d |
|
35 |
|
oveq2 |
|
36 |
|
fveq2 |
|
37 |
36
|
oveq2d |
|
38 |
35 37
|
eqeq12d |
|
39 |
34 38
|
rspc2v |
|
40 |
39
|
impancom |
|
41 |
12 30 40
|
syl2anc |
|
42 |
41
|
imp |
|
43 |
27 42
|
syldan |
|
44 |
43
|
breq1d |
|
45 |
29 44
|
bitrd |
|
46 |
|
f1of1 |
|
47 |
5 46
|
syl |
|
48 |
47
|
adantr |
|
49 |
|
blssm |
|
50 |
19 12 15 49
|
syl3anc |
|
51 |
50
|
adantr |
|
52 |
|
f1elima |
|
53 |
48 27 51 52
|
syl3anc |
|
54 |
11
|
adantr |
|
55 |
14
|
adantr |
|
56 |
|
f1ocnvfv2 |
|
57 |
5 56
|
sylan |
|
58 |
|
simpr |
|
59 |
57 58
|
eqeltrd |
|
60 |
|
elbl2 |
|
61 |
54 21 55 59 60
|
syl22anc |
|
62 |
45 53 61
|
3bitr4d |
|
63 |
57
|
eleq1d |
|
64 |
57
|
eleq1d |
|
65 |
62 63 64
|
3bitr3d |
|
66 |
65
|
ex |
|
67 |
10 18 66
|
pm5.21ndd |
|
68 |
67
|
eqrdv |
|