Step |
Hyp |
Ref |
Expression |
1 |
|
simpll |
|
2 |
1
|
sselda |
|
3 |
|
elinti |
|
4 |
3
|
imp |
|
5 |
4
|
adantll |
|
6 |
|
tskpwss |
|
7 |
2 5 6
|
syl2anc |
|
8 |
7
|
ralrimiva |
|
9 |
|
ssint |
|
10 |
8 9
|
sylibr |
|
11 |
|
tskpw |
|
12 |
2 5 11
|
syl2anc |
|
13 |
12
|
ralrimiva |
|
14 |
|
vpwex |
|
15 |
14
|
elint2 |
|
16 |
13 15
|
sylibr |
|
17 |
10 16
|
jca |
|
18 |
17
|
ralrimiva |
|
19 |
|
elpwi |
|
20 |
|
rexnal |
|
21 |
|
simpr |
|
22 |
|
intex |
|
23 |
21 22
|
sylib |
|
24 |
23
|
ad2antrr |
|
25 |
|
simplr |
|
26 |
|
ssdomg |
|
27 |
24 25 26
|
sylc |
|
28 |
|
vex |
|
29 |
|
intss1 |
|
30 |
29
|
ad2antrl |
|
31 |
|
ssdomg |
|
32 |
28 30 31
|
mpsyl |
|
33 |
|
simprr |
|
34 |
|
simplll |
|
35 |
|
simprl |
|
36 |
34 35
|
sseldd |
|
37 |
25 30
|
sstrd |
|
38 |
|
tsken |
|
39 |
36 37 38
|
syl2anc |
|
40 |
39
|
ord |
|
41 |
33 40
|
mt3d |
|
42 |
41
|
ensymd |
|
43 |
|
domentr |
|
44 |
32 42 43
|
syl2anc |
|
45 |
|
sbth |
|
46 |
27 44 45
|
syl2anc |
|
47 |
46
|
rexlimdvaa |
|
48 |
20 47
|
syl5bir |
|
49 |
48
|
con1d |
|
50 |
|
vex |
|
51 |
50
|
elint2 |
|
52 |
49 51
|
syl6ibr |
|
53 |
52
|
orrd |
|
54 |
19 53
|
sylan2 |
|
55 |
54
|
ralrimiva |
|
56 |
|
eltsk2g |
|
57 |
23 56
|
syl |
|
58 |
18 55 57
|
mpbir2and |
|