Step |
Hyp |
Ref |
Expression |
1 |
|
ghmf1.x |
|
2 |
|
ghmf1.y |
|
3 |
|
ghmf1.z |
|
4 |
|
ghmf1.u |
|
5 |
3 4
|
ghmid |
|
6 |
5
|
ad2antrr |
|
7 |
6
|
eqeq2d |
|
8 |
|
simplr |
|
9 |
|
simpr |
|
10 |
|
ghmgrp1 |
|
11 |
10
|
ad2antrr |
|
12 |
1 3
|
grpidcl |
|
13 |
11 12
|
syl |
|
14 |
|
f1fveq |
|
15 |
8 9 13 14
|
syl12anc |
|
16 |
7 15
|
bitr3d |
|
17 |
16
|
biimpd |
|
18 |
17
|
ralrimiva |
|
19 |
1 2
|
ghmf |
|
20 |
19
|
adantr |
|
21 |
|
eqid |
|
22 |
|
eqid |
|
23 |
1 21 22
|
ghmsub |
|
24 |
23
|
3expb |
|
25 |
24
|
adantlr |
|
26 |
25
|
eqeq1d |
|
27 |
|
fveqeq2 |
|
28 |
|
eqeq1 |
|
29 |
27 28
|
imbi12d |
|
30 |
|
simplr |
|
31 |
10
|
adantr |
|
32 |
1 21
|
grpsubcl |
|
33 |
32
|
3expb |
|
34 |
31 33
|
sylan |
|
35 |
29 30 34
|
rspcdva |
|
36 |
26 35
|
sylbird |
|
37 |
|
ghmgrp2 |
|
38 |
37
|
ad2antrr |
|
39 |
19
|
ad2antrr |
|
40 |
|
simprl |
|
41 |
39 40
|
ffvelrnd |
|
42 |
|
simprr |
|
43 |
39 42
|
ffvelrnd |
|
44 |
2 4 22
|
grpsubeq0 |
|
45 |
38 41 43 44
|
syl3anc |
|
46 |
10
|
ad2antrr |
|
47 |
1 3 21
|
grpsubeq0 |
|
48 |
46 40 42 47
|
syl3anc |
|
49 |
36 45 48
|
3imtr3d |
|
50 |
49
|
ralrimivva |
|
51 |
|
dff13 |
|
52 |
20 50 51
|
sylanbrc |
|
53 |
18 52
|
impbida |
|