Step |
Hyp |
Ref |
Expression |
1 |
|
lsatset.v |
|
2 |
|
lsatset.n |
|
3 |
|
lsatset.z |
|
4 |
|
lsatset.a |
|
5 |
|
elex |
|
6 |
|
fveq2 |
|
7 |
6 1
|
eqtr4di |
|
8 |
|
fveq2 |
|
9 |
8 3
|
eqtr4di |
|
10 |
9
|
sneqd |
|
11 |
7 10
|
difeq12d |
|
12 |
|
fveq2 |
|
13 |
12 2
|
eqtr4di |
|
14 |
13
|
fveq1d |
|
15 |
11 14
|
mpteq12dv |
|
16 |
15
|
rneqd |
|
17 |
|
df-lsatoms |
|
18 |
2
|
fvexi |
|
19 |
18
|
rnex |
|
20 |
|
p0ex |
|
21 |
19 20
|
unex |
|
22 |
|
eqid |
|
23 |
|
fvrn0 |
|
24 |
23
|
a1i |
|
25 |
22 24
|
fmpti |
|
26 |
|
frn |
|
27 |
25 26
|
ax-mp |
|
28 |
21 27
|
ssexi |
|
29 |
16 17 28
|
fvmpt |
|
30 |
5 29
|
syl |
|
31 |
4 30
|
syl5eq |
|