Step |
Hyp |
Ref |
Expression |
1 |
|
disjf1o.xph |
|
2 |
|
disjf1o.f |
|
3 |
|
disjf1o.b |
|
4 |
|
disjf1o.dj |
|
5 |
|
disjf1o.d |
|
6 |
|
disjf1o.e |
|
7 |
|
eqid |
|
8 |
|
simpl |
|
9 |
|
ssrab2 |
|
10 |
5 9
|
eqsstri |
|
11 |
|
id |
|
12 |
10 11
|
sseldi |
|
13 |
12
|
adantl |
|
14 |
8 13 3
|
syl2anc |
|
15 |
11 5
|
eleqtrdi |
|
16 |
|
rabid |
|
17 |
16
|
a1i |
|
18 |
15 17
|
mpbid |
|
19 |
18
|
simprd |
|
20 |
19
|
adantl |
|
21 |
10
|
a1i |
|
22 |
|
disjss1 |
|
23 |
21 4 22
|
sylc |
|
24 |
1 7 14 20 23
|
disjf1 |
|
25 |
|
f1f1orn |
|
26 |
24 25
|
syl |
|
27 |
2
|
a1i |
|
28 |
27
|
reseq1d |
|
29 |
21
|
resmptd |
|
30 |
28 29
|
eqtrd |
|
31 |
|
eqidd |
|
32 |
|
simpl |
|
33 |
|
id |
|
34 |
33 6
|
eleqtrdi |
|
35 |
|
eldifsni |
|
36 |
34 35
|
syl |
|
37 |
36
|
adantl |
|
38 |
|
eldifi |
|
39 |
34 38
|
syl |
|
40 |
2
|
elrnmpt |
|
41 |
39 40
|
syl |
|
42 |
39 41
|
mpbid |
|
43 |
42
|
adantl |
|
44 |
|
nfv |
|
45 |
1 44
|
nfan |
|
46 |
|
nfcv |
|
47 |
|
nfmpt1 |
|
48 |
47
|
nfrn |
|
49 |
46 48
|
nfel |
|
50 |
|
simp3 |
|
51 |
|
simp2 |
|
52 |
|
id |
|
53 |
52
|
eqcomd |
|
54 |
53
|
adantl |
|
55 |
|
simpl |
|
56 |
54 55
|
eqnetrd |
|
57 |
56
|
3adant2 |
|
58 |
51 57
|
jca |
|
59 |
58 16
|
sylibr |
|
60 |
5
|
eqcomi |
|
61 |
60
|
a1i |
|
62 |
59 61
|
eleqtrd |
|
63 |
|
eqvisset |
|
64 |
63
|
3ad2ant3 |
|
65 |
7
|
elrnmpt1 |
|
66 |
62 64 65
|
syl2anc |
|
67 |
50 66
|
eqeltrd |
|
68 |
67
|
3adant1l |
|
69 |
68
|
3exp |
|
70 |
45 49 69
|
rexlimd |
|
71 |
70
|
imp |
|
72 |
32 37 43 71
|
syl21anc |
|
73 |
72
|
ralrimiva |
|
74 |
|
dfss3 |
|
75 |
73 74
|
sylibr |
|
76 |
|
simpl |
|
77 |
|
vex |
|
78 |
7
|
elrnmpt |
|
79 |
77 78
|
ax-mp |
|
80 |
79
|
biimpi |
|
81 |
80
|
adantl |
|
82 |
|
nfv |
|
83 |
|
simpr |
|
84 |
12
|
adantr |
|
85 |
83 63
|
syl |
|
86 |
2
|
elrnmpt1 |
|
87 |
84 85 86
|
syl2anc |
|
88 |
83 87
|
eqeltrd |
|
89 |
88
|
3adant1 |
|
90 |
19
|
adantr |
|
91 |
83 90
|
eqnetrd |
|
92 |
|
nelsn |
|
93 |
91 92
|
syl |
|
94 |
93
|
3adant1 |
|
95 |
89 94
|
eldifd |
|
96 |
95 6
|
eleqtrrdi |
|
97 |
96
|
3exp |
|
98 |
1 82 97
|
rexlimd |
|
99 |
98
|
imp |
|
100 |
76 81 99
|
syl2anc |
|
101 |
75 100
|
eqelssd |
|
102 |
30 31 101
|
f1oeq123d |
|
103 |
26 102
|
mpbird |
|