Step |
Hyp |
Ref |
Expression |
1 |
|
mgmhmf1o.b |
|
2 |
|
mgmhmf1o.c |
|
3 |
|
mgmhmrcl |
|
4 |
3
|
ancomd |
|
5 |
4
|
adantr |
|
6 |
|
f1ocnv |
|
7 |
6
|
adantl |
|
8 |
|
f1of |
|
9 |
7 8
|
syl |
|
10 |
|
simpll |
|
11 |
9
|
adantr |
|
12 |
|
simprl |
|
13 |
11 12
|
ffvelrnd |
|
14 |
|
simprr |
|
15 |
11 14
|
ffvelrnd |
|
16 |
|
eqid |
|
17 |
|
eqid |
|
18 |
1 16 17
|
mgmhmlin |
|
19 |
10 13 15 18
|
syl3anc |
|
20 |
|
simplr |
|
21 |
|
f1ocnvfv2 |
|
22 |
20 12 21
|
syl2anc |
|
23 |
|
f1ocnvfv2 |
|
24 |
20 14 23
|
syl2anc |
|
25 |
22 24
|
oveq12d |
|
26 |
19 25
|
eqtrd |
|
27 |
3
|
simpld |
|
28 |
27
|
adantr |
|
29 |
28
|
adantr |
|
30 |
1 16
|
mgmcl |
|
31 |
29 13 15 30
|
syl3anc |
|
32 |
|
f1ocnvfv |
|
33 |
20 31 32
|
syl2anc |
|
34 |
26 33
|
mpd |
|
35 |
34
|
ralrimivva |
|
36 |
9 35
|
jca |
|
37 |
2 1 17 16
|
ismgmhm |
|
38 |
5 36 37
|
sylanbrc |
|
39 |
1 2
|
mgmhmf |
|
40 |
39
|
adantr |
|
41 |
40
|
ffnd |
|
42 |
2 1
|
mgmhmf |
|
43 |
42
|
adantl |
|
44 |
43
|
ffnd |
|
45 |
|
dff1o4 |
|
46 |
41 44 45
|
sylanbrc |
|
47 |
38 46
|
impbida |
|