Step |
Hyp |
Ref |
Expression |
1 |
|
intex |
|
2 |
1
|
biimpi |
|
3 |
2
|
adantr |
|
4 |
|
intssuni |
|
5 |
4
|
adantr |
|
6 |
|
simpr |
|
7 |
|
elpwi |
|
8 |
|
sigasspw |
|
9 |
|
velpw |
|
10 |
8 9
|
sylibr |
|
11 |
10
|
ssriv |
|
12 |
7 11
|
sstrdi |
|
13 |
6 12
|
syl |
|
14 |
|
sspwuni |
|
15 |
13 14
|
sylib |
|
16 |
5 15
|
sstrd |
|
17 |
|
simpr |
|
18 |
|
simplr |
|
19 |
|
elelpwi |
|
20 |
17 18 19
|
syl2anc |
|
21 |
|
vex |
|
22 |
|
issiga |
|
23 |
21 22
|
ax-mp |
|
24 |
20 23
|
sylib |
|
25 |
24
|
simprd |
|
26 |
25
|
simp1d |
|
27 |
26
|
ralrimiva |
|
28 |
|
n0 |
|
29 |
28
|
biimpi |
|
30 |
29
|
adantr |
|
31 |
20
|
ex |
|
32 |
31
|
eximdv |
|
33 |
30 32
|
mpd |
|
34 |
|
elfvex |
|
35 |
34
|
exlimiv |
|
36 |
33 35
|
syl |
|
37 |
|
elintg |
|
38 |
36 37
|
syl |
|
39 |
27 38
|
mpbird |
|
40 |
|
simpll |
|
41 |
|
simpr |
|
42 |
40 41
|
jca |
|
43 |
|
elinti |
|
44 |
43
|
imp |
|
45 |
44
|
adantll |
|
46 |
25
|
simp2d |
|
47 |
46
|
r19.21bi |
|
48 |
42 45 47
|
syl2anc |
|
49 |
48
|
ralrimiva |
|
50 |
|
difexg |
|
51 |
36 50
|
syl |
|
52 |
51
|
adantr |
|
53 |
|
elintg |
|
54 |
52 53
|
syl |
|
55 |
49 54
|
mpbird |
|
56 |
55
|
ralrimiva |
|
57 |
|
simplll |
|
58 |
|
simpr |
|
59 |
57 58
|
jca |
|
60 |
|
simpllr |
|
61 |
|
elpwi |
|
62 |
|
intss1 |
|
63 |
61 62
|
sylan9ss |
|
64 |
|
velpw |
|
65 |
63 64
|
sylibr |
|
66 |
60 65
|
sylancom |
|
67 |
59 66
|
jca |
|
68 |
|
simplr |
|
69 |
25
|
simp3d |
|
70 |
69
|
r19.21bi |
|
71 |
67 68 70
|
sylc |
|
72 |
71
|
ralrimiva |
|
73 |
|
uniexg |
|
74 |
73
|
ad2antlr |
|
75 |
|
elintg |
|
76 |
74 75
|
syl |
|
77 |
72 76
|
mpbird |
|
78 |
77
|
ex |
|
79 |
78
|
ralrimiva |
|
80 |
39 56 79
|
3jca |
|
81 |
|
issiga |
|
82 |
81
|
biimpar |
|
83 |
3 16 80 82
|
syl12anc |
|