Step |
Hyp |
Ref |
Expression |
1 |
|
omeulem1 |
|
2 |
|
opex |
|
3 |
2
|
isseti |
|
4 |
|
19.41v |
|
5 |
3 4
|
mpbiran |
|
6 |
5
|
rexbii |
|
7 |
|
rexcom4 |
|
8 |
6 7
|
bitr3i |
|
9 |
8
|
rexbii |
|
10 |
|
rexcom4 |
|
11 |
9 10
|
bitri |
|
12 |
1 11
|
sylib |
|
13 |
|
simp2rl |
|
14 |
|
simp3rl |
|
15 |
|
simp2rr |
|
16 |
|
simp3rr |
|
17 |
15 16
|
eqtr4d |
|
18 |
|
simp11 |
|
19 |
|
simp13 |
|
20 |
|
simp2ll |
|
21 |
|
simp2lr |
|
22 |
|
simp3ll |
|
23 |
|
simp3lr |
|
24 |
|
omopth2 |
|
25 |
18 19 20 21 22 23 24
|
syl222anc |
|
26 |
17 25
|
mpbid |
|
27 |
|
opeq12 |
|
28 |
26 27
|
syl |
|
29 |
14 28
|
eqtr4d |
|
30 |
13 29
|
eqtr4d |
|
31 |
30
|
3expia |
|
32 |
31
|
exp4b |
|
33 |
32
|
expd |
|
34 |
33
|
rexlimdvv |
|
35 |
34
|
imp |
|
36 |
35
|
rexlimdvv |
|
37 |
36
|
expimpd |
|
38 |
37
|
alrimivv |
|
39 |
|
opeq1 |
|
40 |
39
|
eqeq2d |
|
41 |
|
oveq2 |
|
42 |
41
|
oveq1d |
|
43 |
42
|
eqeq1d |
|
44 |
40 43
|
anbi12d |
|
45 |
|
opeq2 |
|
46 |
45
|
eqeq2d |
|
47 |
|
oveq2 |
|
48 |
47
|
eqeq1d |
|
49 |
46 48
|
anbi12d |
|
50 |
44 49
|
cbvrex2vw |
|
51 |
|
eqeq1 |
|
52 |
51
|
anbi1d |
|
53 |
52
|
2rexbidv |
|
54 |
50 53
|
syl5bb |
|
55 |
54
|
eu4 |
|
56 |
12 38 55
|
sylanbrc |
|