Step |
Hyp |
Ref |
Expression |
1 |
|
sbcpr.x |
|
2 |
|
sbc5 |
|
3 |
|
preq12 |
|
4 |
3
|
eqcomd |
|
5 |
4
|
eqeq2d |
|
6 |
5
|
biimpa |
|
7 |
6 1
|
syl |
|
8 |
7
|
biimpd |
|
9 |
8
|
expcom |
|
10 |
9
|
expd |
|
11 |
10
|
com24 |
|
12 |
11
|
imp31 |
|
13 |
12
|
alrimiv |
|
14 |
|
vex |
|
15 |
14
|
sbc6 |
|
16 |
13 15
|
sylibr |
|
17 |
16
|
ex |
|
18 |
17
|
alrimiv |
|
19 |
|
vex |
|
20 |
19
|
sbc6 |
|
21 |
18 20
|
sylibr |
|
22 |
21
|
exlimiv |
|
23 |
2 22
|
sylbi |
|
24 |
|
sbc5 |
|
25 |
|
sbc5 |
|
26 |
1
|
bicomd |
|
27 |
6 26
|
syl |
|
28 |
27
|
biimpd |
|
29 |
28
|
expcom |
|
30 |
29
|
com13 |
|
31 |
30
|
expd |
|
32 |
31
|
impcom |
|
33 |
32
|
exlimiv |
|
34 |
25 33
|
sylbi |
|
35 |
34
|
impcom |
|
36 |
35
|
exlimiv |
|
37 |
24 36
|
sylbi |
|
38 |
37
|
alrimiv |
|
39 |
|
prex |
|
40 |
39
|
sbc6 |
|
41 |
38 40
|
sylibr |
|
42 |
23 41
|
impbii |
|