Step |
Hyp |
Ref |
Expression |
1 |
|
ntrcls.o |
|
2 |
|
ntrcls.d |
|
3 |
|
ntrcls.r |
|
4 |
|
sseq1 |
|
5 |
|
fveq2 |
|
6 |
5
|
sseq1d |
|
7 |
4 6
|
imbi12d |
|
8 |
|
sseq2 |
|
9 |
|
fveq2 |
|
10 |
9
|
sseq2d |
|
11 |
8 10
|
imbi12d |
|
12 |
7 11
|
cbvral2vw |
|
13 |
|
ralcom |
|
14 |
12 13
|
bitri |
|
15 |
|
simpl |
|
16 |
2 3
|
ntrclsbex |
|
17 |
15 16
|
syl |
|
18 |
|
difssd |
|
19 |
17 18
|
sselpwd |
|
20 |
|
elpwi |
|
21 |
|
simpl |
|
22 |
|
difssd |
|
23 |
21 22
|
sselpwd |
|
24 |
|
simpr |
|
25 |
24
|
difeq2d |
|
26 |
25
|
eqeq2d |
|
27 |
|
eqcom |
|
28 |
26 27
|
bitrdi |
|
29 |
|
dfss4 |
|
30 |
29
|
biimpi |
|
31 |
30
|
adantl |
|
32 |
23 28 31
|
rspcedvd |
|
33 |
16 20 32
|
syl2an |
|
34 |
|
simpl1 |
|
35 |
34 16
|
syl |
|
36 |
|
difssd |
|
37 |
35 36
|
sselpwd |
|
38 |
|
elpwi |
|
39 |
|
simpl |
|
40 |
|
difssd |
|
41 |
39 40
|
sselpwd |
|
42 |
|
simpr |
|
43 |
42
|
difeq2d |
|
44 |
43
|
eqeq2d |
|
45 |
|
eqcom |
|
46 |
44 45
|
bitrdi |
|
47 |
|
dfss4 |
|
48 |
47
|
biimpi |
|
49 |
48
|
adantl |
|
50 |
41 46 49
|
rspcedvd |
|
51 |
16 38 50
|
syl2an |
|
52 |
51
|
3ad2antl1 |
|
53 |
|
simp12 |
|
54 |
53
|
elpwid |
|
55 |
|
simp2 |
|
56 |
55
|
elpwid |
|
57 |
|
sscon34b |
|
58 |
54 56 57
|
syl2anc |
|
59 |
58
|
bicomd |
|
60 |
|
simp11 |
|
61 |
1 2 3
|
ntrclsiex |
|
62 |
60 61
|
syl |
|
63 |
|
elmapi |
|
64 |
62 63
|
syl |
|
65 |
60 16
|
syl |
|
66 |
|
difssd |
|
67 |
65 66
|
sselpwd |
|
68 |
64 67
|
ffvelrnd |
|
69 |
68
|
elpwid |
|
70 |
|
difssd |
|
71 |
65 70
|
sselpwd |
|
72 |
64 71
|
ffvelrnd |
|
73 |
72
|
elpwid |
|
74 |
|
sscon34b |
|
75 |
69 73 74
|
syl2anc |
|
76 |
59 75
|
imbi12d |
|
77 |
|
simp3 |
|
78 |
|
simp13 |
|
79 |
77 78
|
sseq12d |
|
80 |
77
|
fveq2d |
|
81 |
78
|
fveq2d |
|
82 |
80 81
|
sseq12d |
|
83 |
79 82
|
imbi12d |
|
84 |
1 2 3
|
ntrclsfv1 |
|
85 |
60 84
|
syl |
|
86 |
85
|
fveq1d |
|
87 |
|
eqid |
|
88 |
|
eqid |
|
89 |
1 2 65 62 87 53 88
|
dssmapfv3d |
|
90 |
86 89
|
eqtr3d |
|
91 |
60 3
|
syl |
|
92 |
1 2 91
|
ntrclsfv1 |
|
93 |
92
|
fveq1d |
|
94 |
|
eqid |
|
95 |
1 2 65 62 87 55 94
|
dssmapfv3d |
|
96 |
93 95
|
eqtr3d |
|
97 |
90 96
|
sseq12d |
|
98 |
97
|
imbi2d |
|
99 |
76 83 98
|
3bitr4d |
|
100 |
37 52 99
|
ralxfrd2 |
|
101 |
19 33 100
|
ralxfrd2 |
|
102 |
14 101
|
syl5bb |
|