Step |
Hyp |
Ref |
Expression |
1 |
|
breq2 |
|
2 |
1
|
rexbidv |
|
3 |
|
breq2 |
|
4 |
3
|
rexbidv |
|
5 |
|
breq2 |
|
6 |
5
|
rexbidv |
|
7 |
|
ordom |
|
8 |
|
simpl |
|
9 |
|
0fin |
|
10 |
|
eleq1 |
|
11 |
9 10
|
mpbiri |
|
12 |
11
|
necon3bi |
|
13 |
12
|
adantl |
|
14 |
|
tz7.5 |
|
15 |
7 8 13 14
|
mp3an2i |
|
16 |
|
en0 |
|
17 |
|
incom |
|
18 |
17
|
eqeq1i |
|
19 |
16 18
|
bitri |
|
20 |
19
|
rexbii |
|
21 |
15 20
|
sylibr |
|
22 |
|
simplrl |
|
23 |
|
omsson |
|
24 |
22 23
|
sstrdi |
|
25 |
24
|
ssdifssd |
|
26 |
|
simplr |
|
27 |
|
ssel2 |
|
28 |
|
onfin2 |
|
29 |
|
inss2 |
|
30 |
28 29
|
eqsstri |
|
31 |
|
peano2 |
|
32 |
30 31
|
sseldi |
|
33 |
27 32
|
syl |
|
34 |
33
|
adantlr |
|
35 |
|
ssfi |
|
36 |
35
|
ex |
|
37 |
34 36
|
syl |
|
38 |
26 37
|
mtod |
|
39 |
|
ssdif0 |
|
40 |
39
|
necon3bbii |
|
41 |
38 40
|
sylib |
|
42 |
41
|
ad2ant2lr |
|
43 |
|
onint |
|
44 |
25 42 43
|
syl2anc |
|
45 |
44
|
eldifad |
|
46 |
|
simprr |
|
47 |
|
en2sn |
|
48 |
47
|
el2v |
|
49 |
48
|
a1i |
|
50 |
|
simprl |
|
51 |
22 50
|
sseldd |
|
52 |
|
nnord |
|
53 |
51 52
|
syl |
|
54 |
|
ordirr |
|
55 |
|
elinel1 |
|
56 |
54 55
|
nsyl |
|
57 |
|
disjsn |
|
58 |
56 57
|
sylibr |
|
59 |
53 58
|
syl |
|
60 |
|
nnord |
|
61 |
|
ordirr |
|
62 |
60 61
|
syl |
|
63 |
|
disjsn |
|
64 |
62 63
|
sylibr |
|
65 |
64
|
ad2antrr |
|
66 |
|
unen |
|
67 |
46 49 59 65 66
|
syl22anc |
|
68 |
|
simprr |
|
69 |
|
simplrl |
|
70 |
69 23
|
sstrdi |
|
71 |
|
ordsuc |
|
72 |
53 71
|
sylib |
|
73 |
72
|
adantrr |
|
74 |
|
simp2 |
|
75 |
74
|
ssdifssd |
|
76 |
|
simpl1 |
|
77 |
|
simpr |
|
78 |
76 77
|
eldifd |
|
79 |
78
|
ex |
|
80 |
|
onnmin |
|
81 |
75 79 80
|
syl6an |
|
82 |
81
|
con4d |
|
83 |
82
|
imp |
|
84 |
|
simp3 |
|
85 |
|
ordsucss |
|
86 |
84 85
|
syl |
|
87 |
86
|
imp |
|
88 |
87
|
sscond |
|
89 |
|
intss |
|
90 |
88 89
|
syl |
|
91 |
|
simpl2 |
|
92 |
|
ordelon |
|
93 |
84 92
|
sylan |
|
94 |
|
onmindif |
|
95 |
91 93 94
|
syl2anc |
|
96 |
90 95
|
sseldd |
|
97 |
83 96
|
impbida |
|
98 |
68 70 73 97
|
syl3anc |
|
99 |
|
df-suc |
|
100 |
99
|
eleq2i |
|
101 |
98 100
|
bitrdi |
|
102 |
101
|
expr |
|
103 |
102
|
pm5.32rd |
|
104 |
|
elin |
|
105 |
|
elin |
|
106 |
103 104 105
|
3bitr4g |
|
107 |
106
|
eqrdv |
|
108 |
|
indir |
|
109 |
107 108
|
eqtrdi |
|
110 |
|
snssi |
|
111 |
|
df-ss |
|
112 |
110 111
|
sylib |
|
113 |
112
|
uneq2d |
|
114 |
113
|
ad2antrl |
|
115 |
109 114
|
eqtrd |
|
116 |
|
df-suc |
|
117 |
116
|
a1i |
|
118 |
67 115 117
|
3brtr4d |
|
119 |
|
ineq1 |
|
120 |
119
|
breq1d |
|
121 |
120
|
rspcev |
|
122 |
45 118 121
|
syl2anc |
|
123 |
122
|
rexlimdvaa |
|
124 |
|
ineq1 |
|
125 |
124
|
breq1d |
|
126 |
125
|
cbvrexvw |
|
127 |
123 126
|
syl6ib |
|
128 |
127
|
ex |
|
129 |
2 4 6 21 128
|
finds2 |
|
130 |
129
|
impcom |
|