Step |
Hyp |
Ref |
Expression |
1 |
|
ntrcls.o |
|
2 |
|
ntrcls.d |
|
3 |
|
ntrcls.r |
|
4 |
|
ineq1 |
|
5 |
4
|
fveq2d |
|
6 |
|
fveq2 |
|
7 |
6
|
ineq1d |
|
8 |
5 7
|
eqeq12d |
|
9 |
|
ineq2 |
|
10 |
9
|
fveq2d |
|
11 |
|
fveq2 |
|
12 |
11
|
ineq2d |
|
13 |
10 12
|
eqeq12d |
|
14 |
8 13
|
cbvral2vw |
|
15 |
2 3
|
ntrclsbex |
|
16 |
|
difssd |
|
17 |
15 16
|
sselpwd |
|
18 |
17
|
adantr |
|
19 |
|
elpwi |
|
20 |
15
|
adantr |
|
21 |
|
difssd |
|
22 |
20 21
|
sselpwd |
|
23 |
|
difeq2 |
|
24 |
23
|
eqeq2d |
|
25 |
|
eqcom |
|
26 |
24 25
|
syl6bb |
|
27 |
26
|
adantl |
|
28 |
|
dfss4 |
|
29 |
28
|
biimpi |
|
30 |
29
|
adantl |
|
31 |
22 27 30
|
rspcedvd |
|
32 |
19 31
|
sylan2 |
|
33 |
|
ineq1 |
|
34 |
33
|
fveq2d |
|
35 |
|
fveq2 |
|
36 |
35
|
ineq1d |
|
37 |
34 36
|
eqeq12d |
|
38 |
37
|
ralbidv |
|
39 |
38
|
3ad2ant3 |
|
40 |
|
difssd |
|
41 |
15 40
|
sselpwd |
|
42 |
41
|
ad2antrr |
|
43 |
|
simpll |
|
44 |
|
elpwi |
|
45 |
44
|
adantl |
|
46 |
|
difssd |
|
47 |
15 46
|
sselpwd |
|
48 |
47
|
adantr |
|
49 |
|
difeq2 |
|
50 |
49
|
eqeq2d |
|
51 |
|
eqcom |
|
52 |
50 51
|
syl6bb |
|
53 |
52
|
adantl |
|
54 |
|
dfss4 |
|
55 |
54
|
biimpi |
|
56 |
55
|
adantl |
|
57 |
48 53 56
|
rspcedvd |
|
58 |
43 45 57
|
syl2anc |
|
59 |
|
ineq2 |
|
60 |
|
difundi |
|
61 |
59 60
|
eqtr4di |
|
62 |
61
|
fveq2d |
|
63 |
|
fveq2 |
|
64 |
63
|
ineq2d |
|
65 |
62 64
|
eqeq12d |
|
66 |
65
|
3ad2ant3 |
|
67 |
|
simp1l |
|
68 |
67 15
|
jccir |
|
69 |
|
simp1r |
|
70 |
|
simp2 |
|
71 |
1 2 3
|
ntrclsiex |
|
72 |
|
elmapi |
|
73 |
71 72
|
syl |
|
74 |
73
|
anim1i |
|
75 |
74
|
adantr |
|
76 |
|
simpl |
|
77 |
|
simpr |
|
78 |
|
difssd |
|
79 |
77 78
|
sselpwd |
|
80 |
76 79
|
ffvelrnd |
|
81 |
80
|
elpwid |
|
82 |
|
difssd |
|
83 |
77 82
|
sselpwd |
|
84 |
76 83
|
ffvelrnd |
|
85 |
84
|
elpwid |
|
86 |
|
ssinss1 |
|
87 |
85 86
|
syl |
|
88 |
81 87
|
jca |
|
89 |
|
rcompleq |
|
90 |
75 88 89
|
3syl |
|
91 |
|
simplr |
|
92 |
71
|
ad2antrr |
|
93 |
|
eqid |
|
94 |
|
simprl |
|
95 |
94
|
elpwid |
|
96 |
|
simprr |
|
97 |
96
|
elpwid |
|
98 |
95 97
|
unssd |
|
99 |
91 98
|
sselpwd |
|
100 |
|
eqid |
|
101 |
1 2 91 92 93 99 100
|
dssmapfv3d |
|
102 |
|
simpl |
|
103 |
|
simplr |
|
104 |
71
|
ad2antrr |
|
105 |
|
simpr |
|
106 |
|
eqid |
|
107 |
1 2 103 104 93 105 106
|
dssmapfv3d |
|
108 |
102 107
|
sylan2 |
|
109 |
|
simpr |
|
110 |
|
simplr |
|
111 |
71
|
ad2antrr |
|
112 |
|
simpr |
|
113 |
|
eqid |
|
114 |
1 2 110 111 93 112 113
|
dssmapfv3d |
|
115 |
109 114
|
sylan2 |
|
116 |
108 115
|
uneq12d |
|
117 |
|
difindi |
|
118 |
116 117
|
eqtr4di |
|
119 |
101 118
|
eqeq12d |
|
120 |
|
simpll |
|
121 |
1 2 3
|
ntrclsfv1 |
|
122 |
|
fveq1 |
|
123 |
|
fveq1 |
|
124 |
|
fveq1 |
|
125 |
123 124
|
uneq12d |
|
126 |
122 125
|
eqeq12d |
|
127 |
120 121 126
|
3syl |
|
128 |
90 119 127
|
3bitr2d |
|
129 |
68 69 70 128
|
syl12anc |
|
130 |
66 129
|
bitrd |
|
131 |
42 58 130
|
ralxfrd2 |
|
132 |
131
|
3adant3 |
|
133 |
39 132
|
bitrd |
|
134 |
18 32 133
|
ralxfrd2 |
|
135 |
14 134
|
syl5bb |
|