Step |
Hyp |
Ref |
Expression |
1 |
|
mptbi12f.1 |
|
2 |
|
mptbi12f.2 |
|
3 |
1 2
|
nfeq |
|
4 |
|
eleq2 |
|
5 |
3 4
|
alrimi |
|
6 |
|
ax-5 |
|
7 |
5 6
|
sylg |
|
8 |
|
eqeq2 |
|
9 |
8
|
alrimiv |
|
10 |
9
|
ralimi |
|
11 |
|
df-ral |
|
12 |
10 11
|
sylib |
|
13 |
|
19.21v |
|
14 |
13
|
albii |
|
15 |
12 14
|
sylibr |
|
16 |
|
id |
|
17 |
16
|
alanimi |
|
18 |
17
|
alanimi |
|
19 |
7 15 18
|
syl2an |
|
20 |
|
tsan2 |
|
21 |
20
|
ord |
|
22 |
|
tsbi2 |
|
23 |
22
|
ord |
|
24 |
23
|
a1dd |
|
25 |
|
ax-1 |
|
26 |
24 25
|
contrd |
|
27 |
26
|
a1d |
|
28 |
21 27
|
cnf1dd |
|
29 |
|
simplim |
|
30 |
29
|
a1d |
|
31 |
|
tsbi3 |
|
32 |
31
|
ord |
|
33 |
|
tsan2 |
|
34 |
33
|
a1d |
|
35 |
32 34
|
cnf1dd |
|
36 |
30 35
|
contrd |
|
37 |
36
|
ord |
|
38 |
|
tsan2 |
|
39 |
38
|
a1d |
|
40 |
37 39
|
cnf1dd |
|
41 |
28 40
|
contrd |
|
42 |
41
|
a1d |
|
43 |
29
|
a1d |
|
44 |
|
tsan3 |
|
45 |
44
|
a1d |
|
46 |
43 45
|
cnfn2dd |
|
47 |
42 46
|
mpdd |
|
48 |
|
notnotr |
|
49 |
48
|
a1i |
|
50 |
38
|
a1d |
|
51 |
49 50
|
cnfn2dd |
|
52 |
36
|
a1d |
|
53 |
51 52
|
cnfn2dd |
|
54 |
|
tsan3 |
|
55 |
54
|
a1d |
|
56 |
49 55
|
cnfn2dd |
|
57 |
29
|
a1d |
|
58 |
44
|
a1d |
|
59 |
57 58
|
cnfn2dd |
|
60 |
53 59
|
mpdd |
|
61 |
|
tsbi3 |
|
62 |
61
|
a1d |
|
63 |
60 62
|
cnfn2dd |
|
64 |
56 63
|
cnfn2dd |
|
65 |
53 64
|
jcad |
|
66 |
|
ax-1 |
|
67 |
|
tsim3 |
|
68 |
67
|
a1d |
|
69 |
66 68
|
cnf2dd |
|
70 |
|
tsbi1 |
|
71 |
70
|
a1d |
|
72 |
69 71
|
cnf2dd |
|
73 |
49 72
|
cnfn2dd |
|
74 |
65 73
|
contrd |
|
75 |
74
|
a1d |
|
76 |
26
|
a1d |
|
77 |
75 76
|
cnf2dd |
|
78 |
|
tsan3 |
|
79 |
78
|
a1d |
|
80 |
77 79
|
cnfn2dd |
|
81 |
33
|
a1d |
|
82 |
43 81
|
cnfn2dd |
|
83 |
|
tsbi4 |
|
84 |
83
|
a1d |
|
85 |
82 84
|
cnfn2dd |
|
86 |
42 85
|
cnfn1dd |
|
87 |
|
tsan1 |
|
88 |
87
|
a1d |
|
89 |
75 88
|
cnf2dd |
|
90 |
86 89
|
cnfn1dd |
|
91 |
|
tsbi4 |
|
92 |
91
|
a1d |
|
93 |
92
|
or32dd |
|
94 |
90 93
|
cnf2dd |
|
95 |
80 94
|
cnfn1dd |
|
96 |
47 95
|
contrd |
|
97 |
96
|
efald2 |
|
98 |
97
|
2alimi |
|
99 |
19 98
|
syl |
|
100 |
|
eqopab2bw |
|
101 |
99 100
|
sylibr |
|
102 |
|
df-mpt |
|
103 |
|
df-mpt |
|
104 |
101 102 103
|
3eqtr4g |
|