Step |
Hyp |
Ref |
Expression |
1 |
|
gruina.1 |
|
2 |
|
nss |
|
3 |
|
fveqeq2 |
|
4 |
3
|
rspcev |
|
5 |
4
|
ex |
|
6 |
5
|
ad2antrl |
|
7 |
|
simplr |
|
8 |
|
simprl |
|
9 |
|
r1elssi |
|
10 |
9
|
sseld |
|
11 |
7 8 10
|
sylc |
|
12 |
|
tcrank |
|
13 |
11 12
|
syl |
|
14 |
13
|
eleq2d |
|
15 |
|
gruelss |
|
16 |
|
grutr |
|
17 |
16
|
adantr |
|
18 |
|
vex |
|
19 |
|
tcmin |
|
20 |
18 19
|
ax-mp |
|
21 |
15 17 20
|
syl2anc |
|
22 |
|
rankf |
|
23 |
|
ffun |
|
24 |
22 23
|
ax-mp |
|
25 |
|
fvelima |
|
26 |
24 25
|
mpan |
|
27 |
|
ssrexv |
|
28 |
21 26 27
|
syl2im |
|
29 |
28
|
ad2ant2r |
|
30 |
14 29
|
sylbid |
|
31 |
|
simprr |
|
32 |
|
ne0i |
|
33 |
1
|
gruina |
|
34 |
32 33
|
sylan2 |
|
35 |
|
inawina |
|
36 |
|
winaon |
|
37 |
34 35 36
|
3syl |
|
38 |
|
r1fnon |
|
39 |
|
fndm |
|
40 |
38 39
|
ax-mp |
|
41 |
37 40
|
eleqtrrdi |
|
42 |
41
|
ad2ant2r |
|
43 |
|
rankr1ag |
|
44 |
11 42 43
|
syl2anc |
|
45 |
31 44
|
mtbid |
|
46 |
|
rankon |
|
47 |
|
eloni |
|
48 |
|
eloni |
|
49 |
|
ordtri3or |
|
50 |
47 48 49
|
syl2an |
|
51 |
46 37 50
|
sylancr |
|
52 |
|
3orass |
|
53 |
51 52
|
sylib |
|
54 |
53
|
ord |
|
55 |
54
|
ad2ant2r |
|
56 |
45 55
|
mpd |
|
57 |
6 30 56
|
mpjaod |
|
58 |
57
|
ex |
|
59 |
58
|
exlimdv |
|
60 |
2 59
|
syl5bi |
|
61 |
|
simpll |
|
62 |
|
ne0i |
|
63 |
62 33
|
sylan2 |
|
64 |
63
|
ad2ant2r |
|
65 |
64 35 36
|
3syl |
|
66 |
|
simprl |
|
67 |
|
fveq2 |
|
68 |
67
|
ad2antll |
|
69 |
|
elina |
|
70 |
69
|
simp2bi |
|
71 |
64 70
|
syl |
|
72 |
68 71
|
eqtrd |
|
73 |
|
rankcf |
|
74 |
|
fvex |
|
75 |
|
vex |
|
76 |
|
domtri |
|
77 |
74 75 76
|
mp2an |
|
78 |
73 77
|
mpbir |
|
79 |
72 78
|
eqbrtrrdi |
|
80 |
|
grudomon |
|
81 |
61 65 66 79 80
|
syl112anc |
|
82 |
|
elin |
|
83 |
82
|
biimpri |
|
84 |
83 1
|
eleqtrrdi |
|
85 |
|
ordirr |
|
86 |
48 85
|
syl |
|
87 |
86
|
adantl |
|
88 |
84 87
|
pm2.21dd |
|
89 |
81 65 88
|
syl2anc |
|
90 |
89
|
rexlimdvaa |
|
91 |
60 90
|
syld |
|
92 |
91
|
pm2.18d |
|
93 |
1
|
grur1a |
|
94 |
93
|
adantr |
|
95 |
92 94
|
eqssd |
|