Step |
Hyp |
Ref |
Expression |
1 |
|
ntrcls.o |
|
2 |
|
ntrcls.d |
|
3 |
|
ntrcls.r |
|
4 |
|
fveq2 |
|
5 |
4
|
ineq1d |
|
6 |
|
ineq1 |
|
7 |
6
|
fveq2d |
|
8 |
5 7
|
sseq12d |
|
9 |
|
fveq2 |
|
10 |
9
|
ineq2d |
|
11 |
|
ineq2 |
|
12 |
11
|
fveq2d |
|
13 |
10 12
|
sseq12d |
|
14 |
8 13
|
cbvral2vw |
|
15 |
2 3
|
ntrclsbex |
|
16 |
|
difssd |
|
17 |
15 16
|
sselpwd |
|
18 |
17
|
adantr |
|
19 |
|
elpwi |
|
20 |
|
simpl |
|
21 |
|
difssd |
|
22 |
20 21
|
sselpwd |
|
23 |
|
simpr |
|
24 |
23
|
difeq2d |
|
25 |
24
|
eqeq2d |
|
26 |
|
eqcom |
|
27 |
25 26
|
bitrdi |
|
28 |
|
dfss4 |
|
29 |
28
|
biimpi |
|
30 |
29
|
adantl |
|
31 |
22 27 30
|
rspcedvd |
|
32 |
15 19 31
|
syl2an |
|
33 |
|
simpl1 |
|
34 |
|
difssd |
|
35 |
15 34
|
sselpwd |
|
36 |
33 35
|
syl |
|
37 |
|
elpwi |
|
38 |
|
simpl |
|
39 |
|
difssd |
|
40 |
38 39
|
sselpwd |
|
41 |
|
simpr |
|
42 |
41
|
difeq2d |
|
43 |
42
|
eqeq2d |
|
44 |
|
eqcom |
|
45 |
43 44
|
bitrdi |
|
46 |
|
dfss4 |
|
47 |
46
|
biimpi |
|
48 |
47
|
adantl |
|
49 |
40 45 48
|
rspcedvd |
|
50 |
15 37 49
|
syl2an |
|
51 |
50
|
3ad2antl1 |
|
52 |
|
simp13 |
|
53 |
|
fveq2 |
|
54 |
53
|
ineq1d |
|
55 |
|
ineq1 |
|
56 |
55
|
fveq2d |
|
57 |
54 56
|
sseq12d |
|
58 |
52 57
|
syl |
|
59 |
|
fveq2 |
|
60 |
59
|
ineq2d |
|
61 |
|
ineq2 |
|
62 |
|
difundi |
|
63 |
61 62
|
eqtr4di |
|
64 |
63
|
fveq2d |
|
65 |
60 64
|
sseq12d |
|
66 |
65
|
3ad2ant3 |
|
67 |
|
simp11 |
|
68 |
1 2 3
|
ntrclsiex |
|
69 |
68 15
|
jca |
|
70 |
67 69
|
syl |
|
71 |
|
elmapi |
|
72 |
71
|
adantr |
|
73 |
|
simpr |
|
74 |
|
difssd |
|
75 |
73 74
|
sselpwd |
|
76 |
72 75
|
ffvelrnd |
|
77 |
76
|
elpwid |
|
78 |
|
orc |
|
79 |
|
inss |
|
80 |
77 78 79
|
3syl |
|
81 |
|
difssd |
|
82 |
73 81
|
sselpwd |
|
83 |
72 82
|
ffvelrnd |
|
84 |
83
|
elpwid |
|
85 |
80 84
|
jca |
|
86 |
|
sscon34b |
|
87 |
70 85 86
|
3syl |
|
88 |
|
difindi |
|
89 |
88
|
sseq2i |
|
90 |
89
|
a1i |
|
91 |
67 15
|
syl |
|
92 |
67 68
|
syl |
|
93 |
|
simp12 |
|
94 |
|
rp-simp2 |
|
95 |
|
simpl2 |
|
96 |
|
simpl3 |
|
97 |
|
eqid |
|
98 |
|
simpl |
|
99 |
|
simprl |
|
100 |
99
|
elpwid |
|
101 |
|
simprr |
|
102 |
101
|
elpwid |
|
103 |
100 102
|
unssd |
|
104 |
98 103
|
sselpwd |
|
105 |
104
|
3ad2antl2 |
|
106 |
|
eqid |
|
107 |
1 2 95 96 97 105 106
|
dssmapfv3d |
|
108 |
|
simpl1 |
|
109 |
1 2 3
|
ntrclsfv1 |
|
110 |
109
|
fveq1d |
|
111 |
108 110
|
syl |
|
112 |
107 111
|
eqtr3d |
|
113 |
|
simprl |
|
114 |
|
eqid |
|
115 |
1 2 95 96 97 113 114
|
dssmapfv3d |
|
116 |
109
|
fveq1d |
|
117 |
108 116
|
syl |
|
118 |
115 117
|
eqtr3d |
|
119 |
|
simprr |
|
120 |
|
eqid |
|
121 |
1 2 95 96 97 119 120
|
dssmapfv3d |
|
122 |
109
|
fveq1d |
|
123 |
108 122
|
syl |
|
124 |
121 123
|
eqtr3d |
|
125 |
118 124
|
uneq12d |
|
126 |
112 125
|
sseq12d |
|
127 |
67 91 92 93 94 126
|
syl32anc |
|
128 |
87 90 127
|
3bitrd |
|
129 |
58 66 128
|
3bitrd |
|
130 |
36 51 129
|
ralxfrd2 |
|
131 |
18 32 130
|
ralxfrd2 |
|
132 |
14 131
|
syl5bb |
|