Step |
Hyp |
Ref |
Expression |
1 |
|
simp2 |
|
2 |
|
simp1 |
|
3 |
|
fex |
|
4 |
1 2 3
|
syl2anc |
|
5 |
|
omsval |
|
6 |
4 5
|
syl |
|
7 |
|
simpr |
|
8 |
7
|
sseq1d |
|
9 |
8
|
anbi1d |
|
10 |
9
|
rabbidv |
|
11 |
10
|
mpteq1d |
|
12 |
11
|
rneqd |
|
13 |
12
|
infeq1d |
|
14 |
|
simp3 |
|
15 |
|
fdm |
|
16 |
15
|
3ad2ant2 |
|
17 |
16
|
unieqd |
|
18 |
14 17
|
sseqtrrd |
|
19 |
2
|
uniexd |
|
20 |
|
ssexg |
|
21 |
14 19 20
|
syl2anc |
|
22 |
|
elpwg |
|
23 |
21 22
|
syl |
|
24 |
18 23
|
mpbird |
|
25 |
|
xrltso |
|
26 |
|
iccssxr |
|
27 |
|
soss |
|
28 |
26 27
|
ax-mp |
|
29 |
25 28
|
mp1i |
|
30 |
29
|
infexd |
|
31 |
6 13 24 30
|
fvmptd |
|