Step |
Hyp |
Ref |
Expression |
1 |
|
submrcl |
|
2 |
|
ssinss1 |
|
3 |
2
|
3ad2ant1 |
|
4 |
3
|
ad2antrl |
|
5 |
|
elin |
|
6 |
5
|
simplbi2com |
|
7 |
6
|
3ad2ant2 |
|
8 |
7
|
com12 |
|
9 |
8
|
3ad2ant2 |
|
10 |
9
|
imp |
|
11 |
10
|
adantl |
|
12 |
|
elin |
|
13 |
|
elin |
|
14 |
12 13
|
anbi12i |
|
15 |
|
oveq1 |
|
16 |
15
|
eleq1d |
|
17 |
|
oveq2 |
|
18 |
17
|
eleq1d |
|
19 |
|
simpl |
|
20 |
19
|
adantr |
|
21 |
|
eqidd |
|
22 |
|
simpl |
|
23 |
22
|
adantl |
|
24 |
16 18 20 21 23
|
rspc2vd |
|
25 |
24
|
com12 |
|
26 |
25
|
3ad2ant3 |
|
27 |
26
|
ad2antrl |
|
28 |
27
|
imp |
|
29 |
15
|
eleq1d |
|
30 |
17
|
eleq1d |
|
31 |
|
simpr |
|
32 |
31
|
adantr |
|
33 |
|
eqidd |
|
34 |
|
simpr |
|
35 |
34
|
adantl |
|
36 |
29 30 32 33 35
|
rspc2vd |
|
37 |
36
|
com12 |
|
38 |
37
|
3ad2ant3 |
|
39 |
38
|
adantl |
|
40 |
39
|
adantl |
|
41 |
40
|
imp |
|
42 |
28 41
|
elind |
|
43 |
42
|
ex |
|
44 |
14 43
|
syl5bi |
|
45 |
44
|
ralrimivv |
|
46 |
4 11 45
|
3jca |
|
47 |
46
|
ex |
|
48 |
|
eqid |
|
49 |
|
eqid |
|
50 |
|
eqid |
|
51 |
48 49 50
|
issubm |
|
52 |
48 49 50
|
issubm |
|
53 |
51 52
|
anbi12d |
|
54 |
48 49 50
|
issubm |
|
55 |
47 53 54
|
3imtr4d |
|
56 |
55
|
expd |
|
57 |
1 56
|
mpcom |
|
58 |
57
|
imp |
|