Step |
Hyp |
Ref |
Expression |
1 |
|
cnvresid |
|
2 |
|
cnvnonrel |
|
3 |
|
cnv0 |
|
4 |
2 3
|
eqtr4i |
|
5 |
4
|
dmeqi |
|
6 |
|
df-rn |
|
7 |
|
df-rn |
|
8 |
5 6 7
|
3eqtr4i |
|
9 |
|
0ss |
|
10 |
9
|
rnssi |
|
11 |
8 10
|
eqsstri |
|
12 |
|
ssequn2 |
|
13 |
11 12
|
mpbi |
|
14 |
|
rnun |
|
15 |
|
dfdm4 |
|
16 |
13 14 15
|
3eqtr4ri |
|
17 |
4
|
rneqi |
|
18 |
|
dfdm4 |
|
19 |
|
dfdm4 |
|
20 |
17 18 19
|
3eqtr4i |
|
21 |
|
dmss |
|
22 |
9 21
|
ax-mp |
|
23 |
20 22
|
eqsstri |
|
24 |
|
ssequn2 |
|
25 |
23 24
|
mpbi |
|
26 |
|
dmun |
|
27 |
|
df-rn |
|
28 |
25 26 27
|
3eqtr4ri |
|
29 |
16 28
|
uneq12i |
|
30 |
29
|
equncomi |
|
31 |
30
|
reseq2i |
|
32 |
1 31
|
eqtr2i |
|
33 |
|
cnvss |
|
34 |
32 33
|
eqsstrid |
|
35 |
|
ssun1 |
|
36 |
34 35
|
sstrdi |
|
37 |
|
dmeq |
|
38 |
|
rneq |
|
39 |
37 38
|
uneq12d |
|
40 |
39
|
reseq2d |
|
41 |
|
id |
|
42 |
40 41
|
sseq12d |
|
43 |
36 42
|
syl5ibr |
|
44 |
43
|
adantl |
|
45 |
|
cnvresid |
|
46 |
|
dfdm4 |
|
47 |
|
df-rn |
|
48 |
46 47
|
uneq12i |
|
49 |
48
|
equncomi |
|
50 |
49
|
reseq2i |
|
51 |
45 50
|
eqtr2i |
|
52 |
|
cnvss |
|
53 |
51 52
|
eqsstrid |
|
54 |
|
dmeq |
|
55 |
|
rneq |
|
56 |
54 55
|
uneq12d |
|
57 |
56
|
reseq2d |
|
58 |
|
id |
|
59 |
57 58
|
sseq12d |
|
60 |
53 59
|
syl5ibr |
|
61 |
60
|
adantl |
|
62 |
|
dmeq |
|
63 |
|
rneq |
|
64 |
62 63
|
uneq12d |
|
65 |
64
|
reseq2d |
|
66 |
|
id |
|
67 |
65 66
|
sseq12d |
|
68 |
|
ssun1 |
|
69 |
68
|
a1i |
|
70 |
|
dmexg |
|
71 |
|
rnexg |
|
72 |
|
unexg |
|
73 |
70 71 72
|
syl2anc |
|
74 |
73
|
resiexd |
|
75 |
|
unexg |
|
76 |
74 75
|
mpdan |
|
77 |
|
dmun |
|
78 |
|
ssun1 |
|
79 |
|
dmresi |
|
80 |
79
|
eqimssi |
|
81 |
78 80
|
unssi |
|
82 |
77 81
|
eqsstri |
|
83 |
|
rnun |
|
84 |
|
ssun2 |
|
85 |
|
rnresi |
|
86 |
85
|
eqimssi |
|
87 |
84 86
|
unssi |
|
88 |
83 87
|
eqsstri |
|
89 |
82 88
|
pm3.2i |
|
90 |
|
unss |
|
91 |
|
ssres2 |
|
92 |
90 91
|
sylbi |
|
93 |
|
ssun4 |
|
94 |
89 92 93
|
mp2b |
|
95 |
94
|
a1i |
|
96 |
44 61 67 69 76 95
|
clcnvlem |
|