Step |
Hyp |
Ref |
Expression |
1 |
|
noinfbnd1.1 |
|
2 |
1
|
noinfno |
|
3 |
2
|
3ad2ant2 |
|
4 |
|
nodmord |
|
5 |
|
ordirr |
|
6 |
3 4 5
|
3syl |
|
7 |
|
simpl3l |
|
8 |
|
ndmfv |
|
9 |
|
1n0 |
|
10 |
9
|
necomi |
|
11 |
|
neeq1 |
|
12 |
10 11
|
mpbiri |
|
13 |
12
|
neneqd |
|
14 |
8 13
|
syl |
|
15 |
14
|
con4i |
|
16 |
15
|
adantl |
|
17 |
|
simpl2l |
|
18 |
17 7
|
sseldd |
|
19 |
18
|
adantr |
|
20 |
17
|
adantr |
|
21 |
|
simprl |
|
22 |
20 21
|
sseldd |
|
23 |
3
|
adantr |
|
24 |
|
nodmon |
|
25 |
23 24
|
syl |
|
26 |
25
|
adantr |
|
27 |
|
simpl3r |
|
28 |
27
|
adantr |
|
29 |
|
simpll1 |
|
30 |
|
simpll2 |
|
31 |
|
simpll3 |
|
32 |
|
simpr |
|
33 |
1
|
noinfbnd1lem2 |
|
34 |
29 30 31 32 33
|
syl112anc |
|
35 |
28 34
|
eqtr4d |
|
36 |
|
simplr |
|
37 |
|
simprr |
|
38 |
|
nogesgn1ores |
|
39 |
19 22 26 35 36 37 38
|
syl321anc |
|
40 |
39
|
expr |
|
41 |
40
|
ralrimiva |
|
42 |
|
dmeq |
|
43 |
42
|
eleq2d |
|
44 |
|
breq1 |
|
45 |
44
|
notbid |
|
46 |
|
reseq1 |
|
47 |
46
|
eqeq1d |
|
48 |
45 47
|
imbi12d |
|
49 |
48
|
ralbidv |
|
50 |
43 49
|
anbi12d |
|
51 |
50
|
rspcev |
|
52 |
7 16 41 51
|
syl12anc |
|
53 |
1
|
noinfdm |
|
54 |
53
|
eleq2d |
|
55 |
54
|
3ad2ant1 |
|
56 |
|
eleq1 |
|
57 |
|
suceq |
|
58 |
57
|
reseq2d |
|
59 |
57
|
reseq2d |
|
60 |
58 59
|
eqeq12d |
|
61 |
60
|
imbi2d |
|
62 |
61
|
ralbidv |
|
63 |
56 62
|
anbi12d |
|
64 |
63
|
rexbidv |
|
65 |
64
|
elabg |
|
66 |
3 24 65
|
3syl |
|
67 |
55 66
|
bitrd |
|
68 |
67
|
adantr |
|
69 |
52 68
|
mpbird |
|
70 |
6 69
|
mtand |
|
71 |
70
|
neqned |
|