Step |
Hyp |
Ref |
Expression |
1 |
|
eqid |
|
2 |
|
eqid |
|
3 |
1 2
|
mgmhmf |
|
4 |
3
|
adantr |
|
5 |
4
|
ffnd |
|
6 |
1 2
|
mgmhmf |
|
7 |
6
|
adantl |
|
8 |
7
|
ffnd |
|
9 |
|
fndmin |
|
10 |
5 8 9
|
syl2anc |
|
11 |
|
ssrab2 |
|
12 |
11
|
a1i |
|
13 |
|
mgmhmrcl |
|
14 |
13
|
simpld |
|
15 |
14
|
adantr |
|
16 |
15
|
ad2antrr |
|
17 |
|
simplrl |
|
18 |
|
simprl |
|
19 |
|
eqid |
|
20 |
1 19
|
mgmcl |
|
21 |
16 17 18 20
|
syl3anc |
|
22 |
|
simplrr |
|
23 |
|
simprr |
|
24 |
22 23
|
oveq12d |
|
25 |
|
simplll |
|
26 |
|
eqid |
|
27 |
1 19 26
|
mgmhmlin |
|
28 |
25 17 18 27
|
syl3anc |
|
29 |
|
simpllr |
|
30 |
1 19 26
|
mgmhmlin |
|
31 |
29 17 18 30
|
syl3anc |
|
32 |
24 28 31
|
3eqtr4d |
|
33 |
|
fveq2 |
|
34 |
|
fveq2 |
|
35 |
33 34
|
eqeq12d |
|
36 |
35
|
elrab |
|
37 |
21 32 36
|
sylanbrc |
|
38 |
37
|
expr |
|
39 |
38
|
ralrimiva |
|
40 |
|
fveq2 |
|
41 |
|
fveq2 |
|
42 |
40 41
|
eqeq12d |
|
43 |
42
|
ralrab |
|
44 |
39 43
|
sylibr |
|
45 |
44
|
expr |
|
46 |
45
|
ralrimiva |
|
47 |
|
fveq2 |
|
48 |
|
fveq2 |
|
49 |
47 48
|
eqeq12d |
|
50 |
49
|
ralrab |
|
51 |
46 50
|
sylibr |
|
52 |
1 19
|
issubmgm |
|
53 |
15 52
|
syl |
|
54 |
12 51 53
|
mpbir2and |
|
55 |
10 54
|
eqeltrd |
|