Step |
Hyp |
Ref |
Expression |
1 |
|
xpord3.1 |
|
2 |
|
sexp3.1 |
|
3 |
|
sexp3.2 |
|
4 |
|
sexp3.3 |
|
5 |
|
elxpxp |
|
6 |
|
df-3an |
|
7 |
1
|
xpord3pred |
|
8 |
7
|
adantl |
|
9 |
|
simpr1 |
|
10 |
2
|
adantr |
|
11 |
|
setlikespec |
|
12 |
9 10 11
|
syl2anc |
|
13 |
|
snex |
|
14 |
13
|
a1i |
|
15 |
12 14
|
unexd |
|
16 |
|
simpr2 |
|
17 |
3
|
adantr |
|
18 |
|
setlikespec |
|
19 |
16 17 18
|
syl2anc |
|
20 |
|
snex |
|
21 |
20
|
a1i |
|
22 |
19 21
|
unexd |
|
23 |
15 22
|
xpexd |
|
24 |
|
simpr3 |
|
25 |
4
|
adantr |
|
26 |
|
setlikespec |
|
27 |
24 25 26
|
syl2anc |
|
28 |
|
snex |
|
29 |
28
|
a1i |
|
30 |
27 29
|
unexd |
|
31 |
23 30
|
xpexd |
|
32 |
31
|
difexd |
|
33 |
8 32
|
eqeltrd |
|
34 |
|
predeq3 |
|
35 |
34
|
eleq1d |
|
36 |
35
|
biimprd |
|
37 |
36
|
com12 |
|
38 |
33 37
|
syl |
|
39 |
6 38
|
sylan2br |
|
40 |
39
|
anassrs |
|
41 |
40
|
rexlimdva |
|
42 |
41
|
rexlimdvva |
|
43 |
5 42
|
syl5bi |
|
44 |
43
|
ralrimiv |
|
45 |
|
dfse3 |
|
46 |
44 45
|
sylibr |
|