Step |
Hyp |
Ref |
Expression |
1 |
|
mdexch.1 |
|
2 |
|
mdexch.2 |
|
3 |
|
mdexch.3 |
|
4 |
|
chjass |
|
5 |
3 1 4
|
mp3an12 |
|
6 |
3 1
|
chjcli |
|
7 |
|
chjcom |
|
8 |
6 7
|
mpan2 |
|
9 |
|
chjcl |
|
10 |
1 9
|
mpan |
|
11 |
|
chjcom |
|
12 |
10 3 11
|
sylancl |
|
13 |
5 8 12
|
3eqtr4d |
|
14 |
13
|
ineq1d |
|
15 |
|
inass |
|
16 |
|
incom |
|
17 |
1 2
|
chjcomi |
|
18 |
17
|
ineq2i |
|
19 |
2 1
|
chabs2i |
|
20 |
18 19
|
eqtri |
|
21 |
16 20
|
eqtri |
|
22 |
21
|
ineq2i |
|
23 |
15 22
|
eqtri |
|
24 |
14 23
|
eqtr4di |
|
25 |
24
|
ad2antrr |
|
26 |
|
chlej2 |
|
27 |
26
|
ex |
|
28 |
2 1 27
|
mp3an23 |
|
29 |
1 2
|
chjcli |
|
30 |
|
mdi |
|
31 |
30
|
exp32 |
|
32 |
3 29 31
|
mp3an12 |
|
33 |
10 32
|
syl |
|
34 |
33
|
com23 |
|
35 |
28 34
|
syld |
|
36 |
35
|
imp31 |
|
37 |
36
|
adantrr |
|
38 |
3 29
|
chincli |
|
39 |
|
chlej2 |
|
40 |
39
|
ex |
|
41 |
38 1 40
|
mp3an12 |
|
42 |
10 41
|
syl |
|
43 |
42
|
imp |
|
44 |
|
chjcom |
|
45 |
10 1 44
|
sylancl |
|
46 |
1
|
chjidmi |
|
47 |
46
|
oveq1i |
|
48 |
|
chjass |
|
49 |
1 1 48
|
mp3an12 |
|
50 |
|
chjcom |
|
51 |
1 50
|
mpan |
|
52 |
47 49 51
|
3eqtr3a |
|
53 |
45 52
|
eqtrd |
|
54 |
53
|
adantr |
|
55 |
43 54
|
sseqtrd |
|
56 |
55
|
ad2ant2rl |
|
57 |
37 56
|
eqsstrd |
|
58 |
57
|
ssrind |
|
59 |
25 58
|
eqsstrd |
|
60 |
59
|
adantrl |
|
61 |
|
mdi |
|
62 |
61
|
exp32 |
|
63 |
1 2 62
|
mp3an12 |
|
64 |
63
|
com23 |
|
65 |
64
|
imp31 |
|
66 |
1 3
|
chub2i |
|
67 |
|
ssrin |
|
68 |
66 67
|
ax-mp |
|
69 |
1 2
|
chincli |
|
70 |
6 2
|
chincli |
|
71 |
|
chlej2 |
|
72 |
71
|
ex |
|
73 |
69 70 72
|
mp3an12 |
|
74 |
68 73
|
mpi |
|
75 |
74
|
ad2antrr |
|
76 |
65 75
|
eqsstrd |
|
77 |
76
|
adantrr |
|
78 |
60 77
|
sstrd |
|
79 |
78
|
exp31 |
|
80 |
79
|
com3r |
|
81 |
80
|
3impb |
|
82 |
81
|
ralrimiv |
|
83 |
|
mdbr2 |
|
84 |
6 2 83
|
mp2an |
|
85 |
82 84
|
sylibr |
|
86 |
3 1
|
chjcomi |
|
87 |
|
incom |
|
88 |
18 87 19
|
3eqtr3ri |
|
89 |
86 88
|
ineq12i |
|
90 |
|
inass |
|
91 |
1 2
|
chub1i |
|
92 |
|
mdi |
|
93 |
92
|
exp32 |
|
94 |
3 29 1 93
|
mp3an |
|
95 |
91 94
|
mpi |
|
96 |
1 38
|
chjcomi |
|
97 |
38 1
|
chlejb1i |
|
98 |
97
|
biimpi |
|
99 |
96 98
|
syl5eq |
|
100 |
95 99
|
sylan9eq |
|
101 |
100
|
ineq1d |
|
102 |
90 101
|
syl5eqr |
|
103 |
89 102
|
syl5eq |
|
104 |
103
|
3adant1 |
|
105 |
85 104
|
jca |
|