Step |
Hyp |
Ref |
Expression |
1 |
|
bj-imdirco.exa |
|
2 |
|
bj-imdirco.exb |
|
3 |
|
bj-imdirco.exc |
|
4 |
|
bj-imdirco.arg1 |
|
5 |
|
bj-imdirco.arg2 |
|
6 |
|
imaco |
|
7 |
6
|
eqeq1i |
|
8 |
7
|
anbi2i |
|
9 |
8
|
a1i |
|
10 |
1 2
|
xpexd |
|
11 |
10 4
|
ssexd |
|
12 |
|
imaexg |
|
13 |
11 12
|
syl |
|
14 |
|
imass1 |
|
15 |
|
xpima |
|
16 |
|
simpr |
|
17 |
|
simpr |
|
18 |
16 17
|
orim12i |
|
19 |
|
elif |
|
20 |
|
elun |
|
21 |
18 19 20
|
3imtr4i |
|
22 |
21
|
ssriv |
|
23 |
|
0ss |
|
24 |
|
ssid |
|
25 |
23 24
|
unssi |
|
26 |
22 25
|
sstri |
|
27 |
15 26
|
eqsstri |
|
28 |
14 27
|
sstrdi |
|
29 |
4 28
|
syl |
|
30 |
|
eqidd |
|
31 |
29 30
|
jca |
|
32 |
|
sseq1 |
|
33 |
|
eqeq2 |
|
34 |
32 33
|
anbi12d |
|
35 |
13 31 34
|
spcedv |
|
36 |
35
|
biantrurd |
|
37 |
|
19.41v |
|
38 |
|
anass |
|
39 |
38
|
exbii |
|
40 |
37 39
|
bitr3i |
|
41 |
36 40
|
syl6bb |
|
42 |
|
imaeq2 |
|
43 |
42
|
eqeq1d |
|
44 |
43
|
pm5.32i |
|
45 |
44
|
bianass |
|
46 |
45
|
biancomi |
|
47 |
46
|
exbii |
|
48 |
47
|
a1i |
|
49 |
|
pm4.24 |
|
50 |
49
|
anbi1i |
|
51 |
|
anass |
|
52 |
50 51
|
bitri |
|
53 |
52
|
anbi2i |
|
54 |
|
an12 |
|
55 |
53 54
|
bitri |
|
56 |
55
|
exbii |
|
57 |
56
|
a1i |
|
58 |
41 48 57
|
3bitrd |
|
59 |
58
|
anbi2d |
|
60 |
|
19.42v |
|
61 |
|
anass |
|
62 |
|
ancom |
|
63 |
62
|
bianass |
|
64 |
|
ancom |
|
65 |
|
ancom |
|
66 |
65
|
anbi1i |
|
67 |
66
|
anbi1i |
|
68 |
|
biid |
|
69 |
68
|
bianass |
|
70 |
|
anass |
|
71 |
69 70
|
bitr4i |
|
72 |
|
anass |
|
73 |
67 71 72
|
3bitr4i |
|
74 |
|
anass |
|
75 |
64 73 74
|
3bitr4i |
|
76 |
75
|
anbi2i |
|
77 |
|
anass |
|
78 |
63 76 77
|
3bitr4i |
|
79 |
61 78
|
bitri |
|
80 |
79
|
exbii |
|
81 |
60 80
|
bitr3i |
|
82 |
81
|
a1i |
|
83 |
9 59 82
|
3bitrd |
|
84 |
83
|
opabbidv |
|
85 |
|
bj-opabco |
|
86 |
84 85
|
eqtr4di |
|
87 |
5 4
|
coss12d |
|
88 |
|
bj-xpcossxp |
|
89 |
87 88
|
sstrdi |
|
90 |
1 3 89
|
bj-imdirval2 |
Could not format ( ph -> ( ( A ~P_* C ) ` ( S o. R ) ) = { <. x , z >. | ( ( x C_ A /\ z C_ C ) /\ ( ( S o. R ) " x ) = z ) } ) : No typesetting found for |- ( ph -> ( ( A ~P_* C ) ` ( S o. R ) ) = { <. x , z >. | ( ( x C_ A /\ z C_ C ) /\ ( ( S o. R ) " x ) = z ) } ) with typecode |- |
91 |
2 3 5
|
bj-imdirval2 |
Could not format ( ph -> ( ( B ~P_* C ) ` S ) = { <. y , z >. | ( ( y C_ B /\ z C_ C ) /\ ( S " y ) = z ) } ) : No typesetting found for |- ( ph -> ( ( B ~P_* C ) ` S ) = { <. y , z >. | ( ( y C_ B /\ z C_ C ) /\ ( S " y ) = z ) } ) with typecode |- |
92 |
1 2 4
|
bj-imdirval2 |
Could not format ( ph -> ( ( A ~P_* B ) ` R ) = { <. x , y >. | ( ( x C_ A /\ y C_ B ) /\ ( R " x ) = y ) } ) : No typesetting found for |- ( ph -> ( ( A ~P_* B ) ` R ) = { <. x , y >. | ( ( x C_ A /\ y C_ B ) /\ ( R " x ) = y ) } ) with typecode |- |
93 |
91 92
|
coeq12d |
Could not format ( ph -> ( ( ( B ~P_* C ) ` S ) o. ( ( A ~P_* B ) ` R ) ) = ( { <. y , z >. | ( ( y C_ B /\ z C_ C ) /\ ( S " y ) = z ) } o. { <. x , y >. | ( ( x C_ A /\ y C_ B ) /\ ( R " x ) = y ) } ) ) : No typesetting found for |- ( ph -> ( ( ( B ~P_* C ) ` S ) o. ( ( A ~P_* B ) ` R ) ) = ( { <. y , z >. | ( ( y C_ B /\ z C_ C ) /\ ( S " y ) = z ) } o. { <. x , y >. | ( ( x C_ A /\ y C_ B ) /\ ( R " x ) = y ) } ) ) with typecode |- |
94 |
86 90 93
|
3eqtr4d |
Could not format ( ph -> ( ( A ~P_* C ) ` ( S o. R ) ) = ( ( ( B ~P_* C ) ` S ) o. ( ( A ~P_* B ) ` R ) ) ) : No typesetting found for |- ( ph -> ( ( A ~P_* C ) ` ( S o. R ) ) = ( ( ( B ~P_* C ) ` S ) o. ( ( A ~P_* B ) ` R ) ) ) with typecode |- |