Step |
Hyp |
Ref |
Expression |
1 |
|
ismtyhmeo.1 |
|
2 |
|
ismtyhmeo.2 |
|
3 |
|
ismtyhmeolem.3 |
|
4 |
|
ismtyhmeolem.4 |
|
5 |
|
ismtyhmeolem.5 |
|
6 |
|
isismty |
|
7 |
3 4 6
|
syl2anc |
|
8 |
5 7
|
mpbid |
|
9 |
8
|
simpld |
|
10 |
|
f1of |
|
11 |
9 10
|
syl |
|
12 |
4
|
adantr |
|
13 |
3
|
adantr |
|
14 |
|
ismtycnv |
|
15 |
3 4 14
|
syl2anc |
|
16 |
5 15
|
mpd |
|
17 |
16
|
adantr |
|
18 |
|
simprl |
|
19 |
|
simprr |
|
20 |
|
ismtyima |
|
21 |
12 13 17 18 19 20
|
syl32anc |
|
22 |
|
f1ocnv |
|
23 |
|
f1of |
|
24 |
9 22 23
|
3syl |
|
25 |
|
simpl |
|
26 |
|
ffvelrn |
|
27 |
24 25 26
|
syl2an |
|
28 |
1
|
blopn |
|
29 |
13 27 19 28
|
syl3anc |
|
30 |
21 29
|
eqeltrd |
|
31 |
30
|
ralrimivva |
|
32 |
|
fveq2 |
|
33 |
|
df-ov |
|
34 |
32 33
|
eqtr4di |
|
35 |
34
|
imaeq2d |
|
36 |
35
|
eleq1d |
|
37 |
36
|
ralxp |
|
38 |
31 37
|
sylibr |
|
39 |
|
blf |
|
40 |
|
ffn |
|
41 |
|
imaeq2 |
|
42 |
41
|
eleq1d |
|
43 |
42
|
ralrn |
|
44 |
4 39 40 43
|
4syl |
|
45 |
38 44
|
mpbird |
|
46 |
1
|
mopntopon |
|
47 |
3 46
|
syl |
|
48 |
2
|
mopnval |
|
49 |
4 48
|
syl |
|
50 |
2
|
mopntopon |
|
51 |
4 50
|
syl |
|
52 |
47 49 51
|
tgcn |
|
53 |
11 45 52
|
mpbir2and |
|