Step |
Hyp |
Ref |
Expression |
1 |
|
2sqreultlem |
|
2 |
1
|
ex |
|
3 |
|
2reu2rex |
|
4 |
|
elsni |
|
5 |
|
eqeq2 |
|
6 |
5
|
anbi2d |
|
7 |
6
|
adantl |
|
8 |
|
2sq2 |
|
9 |
|
breq12 |
|
10 |
|
1re |
|
11 |
10
|
ltnri |
|
12 |
11
|
pm2.21i |
|
13 |
9 12
|
syl6bi |
|
14 |
8 13
|
syl6bi |
|
15 |
14
|
impcomd |
|
16 |
15
|
adantr |
|
17 |
7 16
|
sylbid |
|
18 |
17
|
ex |
|
19 |
18
|
com23 |
|
20 |
19
|
rexlimivv |
|
21 |
3 4 20
|
syl2imc |
|
22 |
21
|
a1d |
|
23 |
|
eldif |
|
24 |
|
eldifsnneq |
|
25 |
|
nn0ssz |
|
26 |
|
id |
|
27 |
26
|
eqcomd |
|
28 |
27
|
adantl |
|
29 |
28
|
reximi |
|
30 |
29
|
reximi |
|
31 |
|
ssrexv |
|
32 |
25 31
|
ax-mp |
|
33 |
32
|
reximi |
|
34 |
3 30 33
|
3syl |
|
35 |
|
ssrexv |
|
36 |
25 34 35
|
mpsyl |
|
37 |
36
|
adantl |
|
38 |
|
eldifi |
|
39 |
38
|
adantr |
|
40 |
|
2sqb |
|
41 |
39 40
|
syl |
|
42 |
37 41
|
mpbid |
|
43 |
42
|
ord |
|
44 |
43
|
ex |
|
45 |
24 44
|
mpid |
|
46 |
23 45
|
sylbir |
|
47 |
46
|
expcom |
|
48 |
22 47
|
pm2.61i |
|
49 |
2 48
|
impbid |
|