Step |
Hyp |
Ref |
Expression |
1 |
|
ax6e2nd |
|
2 |
|
ax6e2eq |
|
3 |
1
|
a1d |
|
4 |
|
exmid |
|
5 |
|
jao |
|
6 |
5
|
3imp |
|
7 |
2 3 4 6
|
mp3an |
|
8 |
1 7
|
jaoi |
|
9 |
|
hbnae |
|
10 |
9
|
eximi |
|
11 |
|
nfa1 |
|
12 |
11
|
19.9 |
|
13 |
10 12
|
sylib |
|
14 |
|
sp |
|
15 |
13 14
|
syl |
|
16 |
|
excom |
|
17 |
|
nfa1 |
|
18 |
17
|
nfn |
|
19 |
18
|
19.9 |
|
20 |
|
id |
|
21 |
|
simpr |
|
22 |
|
simpl |
|
23 |
21 22
|
syl |
|
24 |
|
pm13.181 |
|
25 |
24
|
ancoms |
|
26 |
20 23 25
|
syl2an2r |
|
27 |
|
simpr |
|
28 |
21 27
|
syl |
|
29 |
|
neeq2 |
|
30 |
29
|
biimparc |
|
31 |
26 28 30
|
syl2anc |
|
32 |
|
df-ne |
|
33 |
32
|
bicomi |
|
34 |
|
sp |
|
35 |
34
|
con3i |
|
36 |
33 35
|
sylbir |
|
37 |
31 36
|
syl |
|
38 |
37
|
ex |
|
39 |
38
|
alrimiv |
|
40 |
|
exim |
|
41 |
39 40
|
syl |
|
42 |
|
imbi2 |
|
43 |
42
|
biimpa |
|
44 |
19 41 43
|
sylancr |
|
45 |
44
|
alrimiv |
|
46 |
|
exim |
|
47 |
45 46
|
syl |
|
48 |
|
imbi1 |
|
49 |
48
|
biimpar |
|
50 |
16 47 49
|
sylancr |
|
51 |
|
pm3.34 |
|
52 |
15 50 51
|
sylancr |
|
53 |
|
orc |
|
54 |
53
|
imim2i |
|
55 |
52 54
|
syl |
|
56 |
55
|
idiALT |
|
57 |
|
id |
|
58 |
|
ax-1 |
|
59 |
57 58
|
syl |
|
60 |
|
olc |
|
61 |
60
|
imim2i |
|
62 |
59 61
|
syl |
|
63 |
62
|
idiALT |
|
64 |
|
exmidne |
|
65 |
|
jao |
|
66 |
65
|
3imp21 |
|
67 |
56 63 64 66
|
mp3an |
|
68 |
8 67
|
impbii |
|