Step |
Hyp |
Ref |
Expression |
1 |
|
dfiso2.b |
|
2 |
|
dfiso2.h |
|
3 |
|
dfiso2.c |
|
4 |
|
dfiso2.i |
|
5 |
|
dfiso2.x |
|
6 |
|
dfiso2.y |
|
7 |
|
dfiso2.f |
|
8 |
|
dfiso2.1 |
|
9 |
|
dfiso2.o |
Could not format .o. = ( <. X , Y >. ( comp ` C ) X ) : No typesetting found for |- .o. = ( <. X , Y >. ( comp ` C ) X ) with typecode |- |
10 |
|
dfiso2.p |
|
11 |
|
eqid |
|
12 |
1 11 3 5 6 4
|
isoval |
|
13 |
12
|
eleq2d |
|
14 |
|
eqid |
|
15 |
1 11 3 5 6 14
|
invfval |
|
16 |
15
|
dmeqd |
|
17 |
16
|
eleq2d |
|
18 |
|
eqid |
|
19 |
1 2 18 8 14 3 5 6
|
sectfval |
|
20 |
1 2 18 8 14 3 6 5
|
sectfval |
|
21 |
20
|
cnveqd |
|
22 |
|
cnvopab |
|
23 |
21 22
|
eqtrdi |
|
24 |
19 23
|
ineq12d |
|
25 |
|
inopab |
|
26 |
|
an4 |
|
27 |
|
an42 |
|
28 |
|
anidm |
|
29 |
27 28
|
bitri |
|
30 |
29
|
anbi1i |
|
31 |
26 30
|
bitri |
|
32 |
31
|
opabbii |
|
33 |
25 32
|
eqtri |
|
34 |
24 33
|
eqtrdi |
|
35 |
34
|
dmeqd |
|
36 |
|
dmopab |
|
37 |
35 36
|
eqtrdi |
|
38 |
37
|
eleq2d |
|
39 |
|
eleq1 |
|
40 |
39
|
anbi1d |
|
41 |
|
oveq2 |
|
42 |
41
|
eqeq1d |
|
43 |
|
oveq1 |
|
44 |
43
|
eqeq1d |
|
45 |
42 44
|
anbi12d |
|
46 |
40 45
|
anbi12d |
|
47 |
46
|
exbidv |
|
48 |
47
|
elabg |
|
49 |
7 48
|
syl |
|
50 |
7
|
biantrurd |
|
51 |
50
|
bicomd |
|
52 |
9
|
a1i |
Could not format ( ph -> .o. = ( <. X , Y >. ( comp ` C ) X ) ) : No typesetting found for |- ( ph -> .o. = ( <. X , Y >. ( comp ` C ) X ) ) with typecode |- |
53 |
52
|
eqcomd |
Could not format ( ph -> ( <. X , Y >. ( comp ` C ) X ) = .o. ) : No typesetting found for |- ( ph -> ( <. X , Y >. ( comp ` C ) X ) = .o. ) with typecode |- |
54 |
53
|
oveqd |
Could not format ( ph -> ( g ( <. X , Y >. ( comp ` C ) X ) F ) = ( g .o. F ) ) : No typesetting found for |- ( ph -> ( g ( <. X , Y >. ( comp ` C ) X ) F ) = ( g .o. F ) ) with typecode |- |
55 |
54
|
eqeq1d |
Could not format ( ph -> ( ( g ( <. X , Y >. ( comp ` C ) X ) F ) = ( .1. ` X ) <-> ( g .o. F ) = ( .1. ` X ) ) ) : No typesetting found for |- ( ph -> ( ( g ( <. X , Y >. ( comp ` C ) X ) F ) = ( .1. ` X ) <-> ( g .o. F ) = ( .1. ` X ) ) ) with typecode |- |
56 |
10
|
a1i |
|
57 |
56
|
eqcomd |
|
58 |
57
|
oveqd |
|
59 |
58
|
eqeq1d |
|
60 |
55 59
|
anbi12d |
Could not format ( ph -> ( ( ( g ( <. X , Y >. ( comp ` C ) X ) F ) = ( .1. ` X ) /\ ( F ( <. Y , X >. ( comp ` C ) Y ) g ) = ( .1. ` Y ) ) <-> ( ( g .o. F ) = ( .1. ` X ) /\ ( F .* g ) = ( .1. ` Y ) ) ) ) : No typesetting found for |- ( ph -> ( ( ( g ( <. X , Y >. ( comp ` C ) X ) F ) = ( .1. ` X ) /\ ( F ( <. Y , X >. ( comp ` C ) Y ) g ) = ( .1. ` Y ) ) <-> ( ( g .o. F ) = ( .1. ` X ) /\ ( F .* g ) = ( .1. ` Y ) ) ) ) with typecode |- |
61 |
51 60
|
anbi12d |
Could not format ( ph -> ( ( ( F e. ( X H Y ) /\ g e. ( Y H X ) ) /\ ( ( g ( <. X , Y >. ( comp ` C ) X ) F ) = ( .1. ` X ) /\ ( F ( <. Y , X >. ( comp ` C ) Y ) g ) = ( .1. ` Y ) ) ) <-> ( g e. ( Y H X ) /\ ( ( g .o. F ) = ( .1. ` X ) /\ ( F .* g ) = ( .1. ` Y ) ) ) ) ) : No typesetting found for |- ( ph -> ( ( ( F e. ( X H Y ) /\ g e. ( Y H X ) ) /\ ( ( g ( <. X , Y >. ( comp ` C ) X ) F ) = ( .1. ` X ) /\ ( F ( <. Y , X >. ( comp ` C ) Y ) g ) = ( .1. ` Y ) ) ) <-> ( g e. ( Y H X ) /\ ( ( g .o. F ) = ( .1. ` X ) /\ ( F .* g ) = ( .1. ` Y ) ) ) ) ) with typecode |- |
62 |
61
|
exbidv |
Could not format ( ph -> ( E. g ( ( F e. ( X H Y ) /\ g e. ( Y H X ) ) /\ ( ( g ( <. X , Y >. ( comp ` C ) X ) F ) = ( .1. ` X ) /\ ( F ( <. Y , X >. ( comp ` C ) Y ) g ) = ( .1. ` Y ) ) ) <-> E. g ( g e. ( Y H X ) /\ ( ( g .o. F ) = ( .1. ` X ) /\ ( F .* g ) = ( .1. ` Y ) ) ) ) ) : No typesetting found for |- ( ph -> ( E. g ( ( F e. ( X H Y ) /\ g e. ( Y H X ) ) /\ ( ( g ( <. X , Y >. ( comp ` C ) X ) F ) = ( .1. ` X ) /\ ( F ( <. Y , X >. ( comp ` C ) Y ) g ) = ( .1. ` Y ) ) ) <-> E. g ( g e. ( Y H X ) /\ ( ( g .o. F ) = ( .1. ` X ) /\ ( F .* g ) = ( .1. ` Y ) ) ) ) ) with typecode |- |
63 |
|
df-rex |
Could not format ( E. g e. ( Y H X ) ( ( g .o. F ) = ( .1. ` X ) /\ ( F .* g ) = ( .1. ` Y ) ) <-> E. g ( g e. ( Y H X ) /\ ( ( g .o. F ) = ( .1. ` X ) /\ ( F .* g ) = ( .1. ` Y ) ) ) ) : No typesetting found for |- ( E. g e. ( Y H X ) ( ( g .o. F ) = ( .1. ` X ) /\ ( F .* g ) = ( .1. ` Y ) ) <-> E. g ( g e. ( Y H X ) /\ ( ( g .o. F ) = ( .1. ` X ) /\ ( F .* g ) = ( .1. ` Y ) ) ) ) with typecode |- |
64 |
62 63
|
bitr4di |
Could not format ( ph -> ( E. g ( ( F e. ( X H Y ) /\ g e. ( Y H X ) ) /\ ( ( g ( <. X , Y >. ( comp ` C ) X ) F ) = ( .1. ` X ) /\ ( F ( <. Y , X >. ( comp ` C ) Y ) g ) = ( .1. ` Y ) ) ) <-> E. g e. ( Y H X ) ( ( g .o. F ) = ( .1. ` X ) /\ ( F .* g ) = ( .1. ` Y ) ) ) ) : No typesetting found for |- ( ph -> ( E. g ( ( F e. ( X H Y ) /\ g e. ( Y H X ) ) /\ ( ( g ( <. X , Y >. ( comp ` C ) X ) F ) = ( .1. ` X ) /\ ( F ( <. Y , X >. ( comp ` C ) Y ) g ) = ( .1. ` Y ) ) ) <-> E. g e. ( Y H X ) ( ( g .o. F ) = ( .1. ` X ) /\ ( F .* g ) = ( .1. ` Y ) ) ) ) with typecode |- |
65 |
38 49 64
|
3bitrd |
Could not format ( ph -> ( F e. dom ( ( X ( Sect ` C ) Y ) i^i `' ( Y ( Sect ` C ) X ) ) <-> E. g e. ( Y H X ) ( ( g .o. F ) = ( .1. ` X ) /\ ( F .* g ) = ( .1. ` Y ) ) ) ) : No typesetting found for |- ( ph -> ( F e. dom ( ( X ( Sect ` C ) Y ) i^i `' ( Y ( Sect ` C ) X ) ) <-> E. g e. ( Y H X ) ( ( g .o. F ) = ( .1. ` X ) /\ ( F .* g ) = ( .1. ` Y ) ) ) ) with typecode |- |
66 |
13 17 65
|
3bitrd |
Could not format ( ph -> ( F e. ( X I Y ) <-> E. g e. ( Y H X ) ( ( g .o. F ) = ( .1. ` X ) /\ ( F .* g ) = ( .1. ` Y ) ) ) ) : No typesetting found for |- ( ph -> ( F e. ( X I Y ) <-> E. g e. ( Y H X ) ( ( g .o. F ) = ( .1. ` X ) /\ ( F .* g ) = ( .1. ` Y ) ) ) ) with typecode |- |