Step |
Hyp |
Ref |
Expression |
1 |
|
blrnps |
|
2 |
|
elblps |
|
3 |
|
simpl1 |
|
4 |
|
simpl2 |
|
5 |
|
simpr |
|
6 |
|
psmetcl |
|
7 |
3 4 5 6
|
syl3anc |
|
8 |
|
simpl3 |
|
9 |
|
qbtwnxr |
|
10 |
9
|
3expia |
|
11 |
7 8 10
|
syl2anc |
|
12 |
|
qre |
|
13 |
|
simpll1 |
|
14 |
|
simplr |
|
15 |
|
simpll2 |
|
16 |
|
psmetsym |
|
17 |
13 14 15 16
|
syl3anc |
|
18 |
|
simprrl |
|
19 |
17 18
|
eqbrtrd |
|
20 |
|
simprl |
|
21 |
|
psmetcl |
|
22 |
13 14 15 21
|
syl3anc |
|
23 |
|
rexr |
|
24 |
23
|
ad2antrl |
|
25 |
22 24 19
|
xrltled |
|
26 |
|
psmetlecl |
|
27 |
13 14 15 20 25 26
|
syl122anc |
|
28 |
|
difrp |
|
29 |
27 20 28
|
syl2anc |
|
30 |
19 29
|
mpbid |
|
31 |
20 27
|
resubcld |
|
32 |
22
|
xrleidd |
|
33 |
20
|
recnd |
|
34 |
27
|
recnd |
|
35 |
33 34
|
nncand |
|
36 |
32 35
|
breqtrrd |
|
37 |
|
blss2ps |
|
38 |
13 14 15 31 20 36 37
|
syl33anc |
|
39 |
|
simpll3 |
|
40 |
|
simprrr |
|
41 |
24 39 40
|
xrltled |
|
42 |
|
ssblps |
|
43 |
13 15 24 39 41 42
|
syl221anc |
|
44 |
38 43
|
sstrd |
|
45 |
|
oveq2 |
|
46 |
45
|
sseq1d |
|
47 |
46
|
rspcev |
|
48 |
30 44 47
|
syl2anc |
|
49 |
48
|
expr |
|
50 |
12 49
|
sylan2 |
|
51 |
50
|
rexlimdva |
|
52 |
11 51
|
syld |
|
53 |
52
|
expimpd |
|
54 |
2 53
|
sylbid |
|
55 |
|
eleq2 |
|
56 |
|
sseq2 |
|
57 |
56
|
rexbidv |
|
58 |
55 57
|
imbi12d |
|
59 |
54 58
|
syl5ibrcom |
|
60 |
59
|
3expib |
|
61 |
60
|
rexlimdvv |
|
62 |
1 61
|
sylbid |
|
63 |
62
|
3imp |
|