Step |
Hyp |
Ref |
Expression |
1 |
|
monotuz.1 |
|
2 |
|
monotuz.2 |
|
3 |
|
monotuz.3 |
|
4 |
|
monotuz.4 |
|
5 |
|
monotuz.5 |
|
6 |
|
monotuz.6 |
|
7 |
|
monotuz.7 |
|
8 |
|
csbeq1 |
|
9 |
|
csbeq1 |
|
10 |
|
csbeq1 |
|
11 |
|
uzssz |
|
12 |
|
zssre |
|
13 |
11 12
|
sstri |
|
14 |
3 13
|
eqsstri |
|
15 |
|
nfv |
|
16 |
|
nfcsb1v |
|
17 |
16
|
nfel1 |
|
18 |
15 17
|
nfim |
|
19 |
|
eleq1 |
|
20 |
19
|
anbi2d |
|
21 |
|
csbeq1a |
|
22 |
21
|
eleq1d |
|
23 |
20 22
|
imbi12d |
|
24 |
18 23 2
|
chvarfv |
|
25 |
|
simpl |
|
26 |
25
|
adantlrr |
|
27 |
3 11
|
eqsstri |
|
28 |
|
simplrl |
|
29 |
27 28
|
sseldi |
|
30 |
|
simplrr |
|
31 |
27 30
|
sseldi |
|
32 |
|
simpr |
|
33 |
|
csbeq1 |
|
34 |
33
|
breq2d |
|
35 |
34
|
imbi2d |
|
36 |
|
csbeq1 |
|
37 |
36
|
breq2d |
|
38 |
37
|
imbi2d |
|
39 |
|
csbeq1 |
|
40 |
39
|
breq2d |
|
41 |
40
|
imbi2d |
|
42 |
|
csbeq1 |
|
43 |
42
|
breq2d |
|
44 |
43
|
imbi2d |
|
45 |
|
eleq1 |
|
46 |
45
|
anbi2d |
|
47 |
|
vex |
|
48 |
47 5
|
csbie |
|
49 |
|
csbeq1 |
|
50 |
48 49
|
eqtr3id |
|
51 |
|
ovex |
|
52 |
51 4
|
csbie |
|
53 |
|
oveq1 |
|
54 |
53
|
csbeq1d |
|
55 |
52 54
|
eqtr3id |
|
56 |
50 55
|
breq12d |
|
57 |
46 56
|
imbi12d |
|
58 |
57 1
|
vtoclg |
|
59 |
24
|
3ad2ant2 |
|
60 |
|
simp2l |
|
61 |
|
zre |
|
62 |
61
|
3ad2ant1 |
|
63 |
|
zre |
|
64 |
63
|
3ad2ant2 |
|
65 |
|
simp3 |
|
66 |
62 64 65
|
ltled |
|
67 |
66
|
3ad2ant1 |
|
68 |
|
simp11 |
|
69 |
|
simp12 |
|
70 |
|
eluz |
|
71 |
68 69 70
|
syl2anc |
|
72 |
67 71
|
mpbird |
|
73 |
|
simp2r |
|
74 |
73 3
|
eleqtrdi |
|
75 |
|
uztrn |
|
76 |
72 74 75
|
syl2anc |
|
77 |
76 3
|
eleqtrrdi |
|
78 |
|
nfv |
|
79 |
|
nfcsb1v |
|
80 |
79
|
nfel1 |
|
81 |
78 80
|
nfim |
|
82 |
|
eleq1 |
|
83 |
82
|
anbi2d |
|
84 |
|
csbeq1a |
|
85 |
84
|
eleq1d |
|
86 |
83 85
|
imbi12d |
|
87 |
81 86 2
|
chvarfv |
|
88 |
60 77 87
|
syl2anc |
|
89 |
|
peano2uz |
|
90 |
76 89
|
syl |
|
91 |
90 3
|
eleqtrrdi |
|
92 |
|
nfv |
|
93 |
|
nfcsb1v |
|
94 |
93
|
nfel1 |
|
95 |
92 94
|
nfim |
|
96 |
|
ovex |
|
97 |
|
eleq1 |
|
98 |
97
|
anbi2d |
|
99 |
|
csbeq1a |
|
100 |
99
|
eleq1d |
|
101 |
98 100
|
imbi12d |
|
102 |
95 96 101 2
|
vtoclf |
|
103 |
60 91 102
|
syl2anc |
|
104 |
|
simp3 |
|
105 |
|
nfv |
|
106 |
|
eleq1 |
|
107 |
106
|
anbi2d |
|
108 |
|
csbeq1 |
|
109 |
48 108
|
eqtr3id |
|
110 |
|
oveq1 |
|
111 |
110
|
csbeq1d |
|
112 |
52 111
|
eqtr3id |
|
113 |
109 112
|
breq12d |
|
114 |
107 113
|
imbi12d |
|
115 |
105 114 1
|
chvarfv |
|
116 |
60 77 115
|
syl2anc |
|
117 |
59 88 103 104 116
|
lttrd |
|
118 |
117
|
3exp |
|
119 |
118
|
a2d |
|
120 |
35 38 41 44 58 119
|
uzind2 |
|
121 |
29 31 32 120
|
syl3anc |
|
122 |
26 121
|
mpd |
|
123 |
122
|
ex |
|
124 |
8 9 10 14 24 123
|
ltord1 |
|
125 |
|
nfcvd |
|
126 |
125 6
|
csbiegf |
|
127 |
|
nfcvd |
|
128 |
127 7
|
csbiegf |
|
129 |
126 128
|
breqan12d |
|
130 |
129
|
adantl |
|
131 |
124 130
|
bitrd |
|