Step |
Hyp |
Ref |
Expression |
1 |
|
ssralv |
|
2 |
|
dfon2lem8 |
|
3 |
2
|
simprd |
|
4 |
|
intss1 |
|
5 |
2
|
simpld |
|
6 |
|
intex |
|
7 |
|
dfon2lem3 |
|
8 |
7
|
imp |
|
9 |
8
|
simprd |
|
10 |
|
untelirr |
|
11 |
9 10
|
syl |
|
12 |
|
eleq1 |
|
13 |
12
|
notbid |
|
14 |
11 13
|
syl5ibcom |
|
15 |
14
|
a1dd |
|
16 |
8
|
simpld |
|
17 |
|
trss |
|
18 |
16 17
|
syl |
|
19 |
|
eqss |
|
20 |
19
|
simplbi2com |
|
21 |
18 20
|
syl6 |
|
22 |
21
|
com23 |
|
23 |
|
con3 |
|
24 |
22 23
|
syl6 |
|
25 |
24
|
com23 |
|
26 |
15 25
|
pm2.61d |
|
27 |
6 26
|
sylanb |
|
28 |
5 27
|
syldan |
|
29 |
4 28
|
syl5 |
|
30 |
29
|
ralrimiv |
|
31 |
|
eleq2 |
|
32 |
31
|
notbid |
|
33 |
32
|
ralbidv |
|
34 |
33
|
rspcev |
|
35 |
3 30 34
|
syl2anc |
|
36 |
35
|
expcom |
|
37 |
1 36
|
syl6com |
|
38 |
37
|
impd |
|
39 |
38
|
alrimiv |
|
40 |
|
df-fr |
|
41 |
|
epel |
|
42 |
41
|
notbii |
|
43 |
42
|
ralbii |
|
44 |
43
|
rexbii |
|
45 |
44
|
imbi2i |
|
46 |
45
|
albii |
|
47 |
40 46
|
bitri |
|
48 |
39 47
|
sylibr |
|