Step |
Hyp |
Ref |
Expression |
1 |
|
drhmsubc.c |
|
2 |
|
drhmsubc.j |
|
3 |
|
fldhmsubc.d |
|
4 |
|
fldhmsubc.f |
|
5 |
|
elin |
|
6 |
5
|
simprbi |
|
7 |
|
crngring |
|
8 |
6 7
|
syl |
|
9 |
|
df-field |
|
10 |
8 9
|
eleq2s |
|
11 |
10
|
rgen |
|
12 |
11 3 4
|
srhmsubc |
|
13 |
|
inss1 |
|
14 |
9 13
|
eqsstri |
|
15 |
|
sslin |
|
16 |
14 15
|
ax-mp |
|
17 |
16
|
a1i |
|
18 |
3 1
|
sseq12i |
|
19 |
17 18
|
sylibr |
|
20 |
|
ssidd |
|
21 |
4
|
a1i |
|
22 |
|
oveq12 |
|
23 |
22
|
adantl |
|
24 |
|
simprl |
|
25 |
|
simpr |
|
26 |
25
|
adantl |
|
27 |
|
ovexd |
|
28 |
21 23 24 26 27
|
ovmpod |
|
29 |
2
|
a1i |
|
30 |
16 18
|
mpbir |
|
31 |
30
|
sseli |
|
32 |
31
|
ad2antrl |
|
33 |
30
|
sseli |
|
34 |
33
|
adantl |
|
35 |
34
|
adantl |
|
36 |
29 23 32 35 27
|
ovmpod |
|
37 |
20 28 36
|
3sstr4d |
|
38 |
37
|
ralrimivva |
|
39 |
|
ovex |
|
40 |
4 39
|
fnmpoi |
|
41 |
40
|
a1i |
|
42 |
2 39
|
fnmpoi |
|
43 |
42
|
a1i |
|
44 |
|
inex1g |
|
45 |
1 44
|
eqeltrid |
|
46 |
41 43 45
|
isssc |
|
47 |
19 38 46
|
mpbir2and |
|
48 |
1 2
|
drhmsubc |
|
49 |
|
eqid |
|
50 |
49
|
subsubc |
|
51 |
48 50
|
syl |
|
52 |
12 47 51
|
mpbir2and |
|