Step |
Hyp |
Ref |
Expression |
1 |
|
dmres |
|
2 |
|
simp11 |
|
3 |
|
nodmord |
|
4 |
2 3
|
syl |
|
5 |
|
ndmfv |
|
6 |
|
1n0 |
|
7 |
6
|
necomi |
|
8 |
|
neeq1 |
|
9 |
7 8
|
mpbiri |
|
10 |
9
|
neneqd |
|
11 |
5 10
|
syl |
|
12 |
11
|
con4i |
|
13 |
12
|
adantl |
|
14 |
13
|
3ad2ant2 |
|
15 |
|
ordsucss |
|
16 |
4 14 15
|
sylc |
|
17 |
|
df-ss |
|
18 |
16 17
|
sylib |
|
19 |
1 18
|
syl5eq |
|
20 |
|
dmres |
|
21 |
|
simp12 |
|
22 |
|
nodmord |
|
23 |
21 22
|
syl |
|
24 |
|
nogesgn1o |
|
25 |
|
ndmfv |
|
26 |
|
neeq1 |
|
27 |
7 26
|
mpbiri |
|
28 |
27
|
neneqd |
|
29 |
25 28
|
syl |
|
30 |
29
|
con4i |
|
31 |
24 30
|
syl |
|
32 |
|
ordsucss |
|
33 |
23 31 32
|
sylc |
|
34 |
|
df-ss |
|
35 |
33 34
|
sylib |
|
36 |
20 35
|
syl5eq |
|
37 |
19 36
|
eqtr4d |
|
38 |
19
|
eleq2d |
|
39 |
|
vex |
|
40 |
39
|
elsuc |
|
41 |
|
simpl2l |
|
42 |
41
|
fveq1d |
|
43 |
|
simpr |
|
44 |
43
|
fvresd |
|
45 |
43
|
fvresd |
|
46 |
42 44 45
|
3eqtr3d |
|
47 |
46
|
ex |
|
48 |
|
simp2r |
|
49 |
48 24
|
eqtr4d |
|
50 |
|
fveq2 |
|
51 |
|
fveq2 |
|
52 |
50 51
|
eqeq12d |
|
53 |
49 52
|
syl5ibrcom |
|
54 |
47 53
|
jaod |
|
55 |
40 54
|
syl5bi |
|
56 |
55
|
imp |
|
57 |
|
simpr |
|
58 |
57
|
fvresd |
|
59 |
57
|
fvresd |
|
60 |
56 58 59
|
3eqtr4d |
|
61 |
60
|
ex |
|
62 |
38 61
|
sylbid |
|
63 |
62
|
ralrimiv |
|
64 |
|
nofun |
|
65 |
2 64
|
syl |
|
66 |
65
|
funresd |
|
67 |
|
nofun |
|
68 |
21 67
|
syl |
|
69 |
68
|
funresd |
|
70 |
|
eqfunfv |
|
71 |
66 69 70
|
syl2anc |
|
72 |
37 63 71
|
mpbir2and |
|