Step |
Hyp |
Ref |
Expression |
1 |
|
1n0 |
|
2 |
1
|
neii |
|
3 |
|
eqtr2 |
|
4 |
2 3
|
mto |
|
5 |
|
1on |
|
6 |
|
0elon |
|
7 |
|
df-2o |
|
8 |
|
df-1o |
|
9 |
7 8
|
eqeq12i |
|
10 |
|
suc11 |
|
11 |
9 10
|
syl5bb |
|
12 |
5 6 11
|
mp2an |
|
13 |
1 12
|
nemtbir |
|
14 |
|
eqtr2 |
|
15 |
14
|
ancoms |
|
16 |
13 15
|
mto |
|
17 |
|
nsuceq0 |
|
18 |
7
|
eqeq1i |
|
19 |
17 18
|
nemtbir |
|
20 |
|
eqtr2 |
|
21 |
20
|
ancoms |
|
22 |
19 21
|
mto |
|
23 |
4 16 22
|
3pm3.2ni |
|
24 |
|
vex |
|
25 |
24 24
|
brtp |
|
26 |
23 25
|
mtbir |
|
27 |
26
|
a1i |
|
28 |
|
vex |
|
29 |
24 28
|
brtp |
|
30 |
|
vex |
|
31 |
28 30
|
brtp |
|
32 |
|
eqtr2 |
|
33 |
2 32
|
mto |
|
34 |
33
|
pm2.21i |
|
35 |
34
|
ad2ant2rl |
|
36 |
35
|
expcom |
|
37 |
34
|
ad2ant2rl |
|
38 |
37
|
expcom |
|
39 |
|
3mix2 |
|
40 |
39
|
ad2ant2rl |
|
41 |
40
|
ex |
|
42 |
36 38 41
|
3jaod |
|
43 |
|
eqtr2 |
|
44 |
13 43
|
mto |
|
45 |
44
|
pm2.21i |
|
46 |
45
|
ad2ant2lr |
|
47 |
46
|
ex |
|
48 |
45
|
ad2ant2lr |
|
49 |
48
|
ex |
|
50 |
|
eqtr2 |
|
51 |
19 50
|
mto |
|
52 |
51
|
pm2.21i |
|
53 |
52
|
ad2ant2lr |
|
54 |
53
|
ex |
|
55 |
47 49 54
|
3jaod |
|
56 |
45
|
ad2ant2lr |
|
57 |
56
|
ex |
|
58 |
45
|
ad2ant2lr |
|
59 |
58
|
ex |
|
60 |
52
|
ad2ant2lr |
|
61 |
60
|
ex |
|
62 |
57 59 61
|
3jaod |
|
63 |
42 55 62
|
3jaoi |
|
64 |
63
|
imp |
|
65 |
29 31 64
|
syl2anb |
|
66 |
24 30
|
brtp |
|
67 |
65 66
|
sylibr |
|
68 |
67
|
a1i |
|
69 |
24
|
eltp |
|
70 |
28
|
eltp |
|
71 |
|
eqtr3 |
|
72 |
71
|
3mix2d |
|
73 |
72
|
ex |
|
74 |
|
3mix2 |
|
75 |
74
|
3mix1d |
|
76 |
75
|
ex |
|
77 |
|
3mix1 |
|
78 |
77
|
3mix1d |
|
79 |
78
|
ex |
|
80 |
73 76 79
|
3jaod |
|
81 |
|
3mix2 |
|
82 |
81
|
3mix3d |
|
83 |
82
|
expcom |
|
84 |
|
eqtr3 |
|
85 |
84
|
3mix2d |
|
86 |
85
|
ex |
|
87 |
|
3mix3 |
|
88 |
87
|
3mix3d |
|
89 |
88
|
expcom |
|
90 |
83 86 89
|
3jaod |
|
91 |
|
3mix1 |
|
92 |
91
|
3mix3d |
|
93 |
92
|
expcom |
|
94 |
|
3mix3 |
|
95 |
94
|
3mix1d |
|
96 |
95
|
ex |
|
97 |
|
eqtr3 |
|
98 |
97
|
3mix2d |
|
99 |
98
|
ex |
|
100 |
93 96 99
|
3jaod |
|
101 |
80 90 100
|
3jaoi |
|
102 |
101
|
imp |
|
103 |
69 70 102
|
syl2anb |
|
104 |
|
biid |
|
105 |
28 24
|
brtp |
|
106 |
29 104 105
|
3orbi123i |
|
107 |
103 106
|
sylibr |
|
108 |
27 68 107
|
issoi |
|
109 |
|
df-tp |
|
110 |
|
soeq2 |
|
111 |
109 110
|
ax-mp |
|
112 |
108 111
|
mpbi |
|