Step |
Hyp |
Ref |
Expression |
1 |
|
nosepne |
|
2 |
1
|
neneqd |
|
3 |
|
nodmord |
|
4 |
3
|
3ad2ant1 |
|
5 |
|
ordn2lp |
|
6 |
4 5
|
syl |
|
7 |
|
imnan |
|
8 |
6 7
|
sylibr |
|
9 |
8
|
imp |
|
10 |
|
ndmfv |
|
11 |
9 10
|
syl |
|
12 |
|
nosepeq |
|
13 |
|
simpl1 |
|
14 |
13 3
|
syl |
|
15 |
|
ordirr |
|
16 |
|
ndmfv |
|
17 |
14 15 16
|
3syl |
|
18 |
17
|
eqeq1d |
|
19 |
|
eqcom |
|
20 |
18 19
|
bitrdi |
|
21 |
|
simpl2 |
|
22 |
|
nofun |
|
23 |
21 22
|
syl |
|
24 |
|
nosgnn0 |
|
25 |
|
norn |
|
26 |
21 25
|
syl |
|
27 |
26
|
sseld |
|
28 |
24 27
|
mtoi |
|
29 |
|
funeldmb |
|
30 |
23 28 29
|
syl2anc |
|
31 |
30
|
necon2bbid |
|
32 |
|
nodmord |
|
33 |
32
|
3ad2ant2 |
|
34 |
|
ordtr1 |
|
35 |
33 34
|
syl |
|
36 |
35
|
expdimp |
|
37 |
36
|
con3d |
|
38 |
31 37
|
sylbid |
|
39 |
20 38
|
sylbid |
|
40 |
12 39
|
mpd |
|
41 |
|
ndmfv |
|
42 |
40 41
|
syl |
|
43 |
11 42
|
eqtr4d |
|
44 |
2 43
|
mtand |
|
45 |
|
nosepon |
|
46 |
|
nodmon |
|
47 |
46
|
3ad2ant1 |
|
48 |
|
ontri1 |
|
49 |
45 47 48
|
syl2anc |
|
50 |
44 49
|
mpbird |
|