Step |
Hyp |
Ref |
Expression |
1 |
|
expcllem.1 |
|
2 |
|
expcllem.2 |
|
3 |
|
expcllem.3 |
|
4 |
|
expcl2lem.4 |
|
5 |
|
elznn0nn |
|
6 |
1 2 3
|
expcllem |
|
7 |
6
|
ex |
|
8 |
7
|
adantr |
|
9 |
|
simpll |
|
10 |
1 9
|
sseldi |
|
11 |
|
simprl |
|
12 |
11
|
recnd |
|
13 |
|
nnnn0 |
|
14 |
13
|
ad2antll |
|
15 |
|
expneg2 |
|
16 |
10 12 14 15
|
syl3anc |
|
17 |
|
difss |
|
18 |
|
simpl |
|
19 |
|
eldifsn |
|
20 |
18 19
|
sylibr |
|
21 |
17 1
|
sstri |
|
22 |
17
|
sseli |
|
23 |
17
|
sseli |
|
24 |
22 23 2
|
syl2an |
|
25 |
|
eldifsn |
|
26 |
1
|
sseli |
|
27 |
26
|
anim1i |
|
28 |
25 27
|
sylbi |
|
29 |
|
eldifsn |
|
30 |
1
|
sseli |
|
31 |
30
|
anim1i |
|
32 |
29 31
|
sylbi |
|
33 |
|
mulne0 |
|
34 |
28 32 33
|
syl2an |
|
35 |
|
eldifsn |
|
36 |
24 34 35
|
sylanbrc |
|
37 |
|
ax-1ne0 |
|
38 |
|
eldifsn |
|
39 |
3 37 38
|
mpbir2an |
|
40 |
21 36 39
|
expcllem |
|
41 |
20 14 40
|
syl2anc |
|
42 |
17 41
|
sseldi |
|
43 |
|
eldifsn |
|
44 |
41 43
|
sylib |
|
45 |
44
|
simprd |
|
46 |
|
neeq1 |
|
47 |
|
oveq2 |
|
48 |
47
|
eleq1d |
|
49 |
46 48
|
imbi12d |
|
50 |
4
|
ex |
|
51 |
49 50
|
vtoclga |
|
52 |
42 45 51
|
sylc |
|
53 |
16 52
|
eqeltrd |
|
54 |
53
|
ex |
|
55 |
8 54
|
jaod |
|
56 |
5 55
|
syl5bi |
|
57 |
56
|
3impia |
|