Step |
Hyp |
Ref |
Expression |
1 |
|
zarclsx.1 |
Could not format V = ( i e. ( LIdeal ` R ) |-> { j e. ( PrmIdeal ` R ) | i C_ j } ) : No typesetting found for |- V = ( i e. ( LIdeal ` R ) |-> { j e. ( PrmIdeal ` R ) | i C_ j } ) with typecode |- |
2 |
|
crngring |
|
3 |
2
|
ad4antr |
|
4 |
|
elpwi |
|
5 |
4
|
adantl |
|
6 |
5
|
adantr |
|
7 |
6
|
sselda |
|
8 |
|
eqid |
|
9 |
|
eqid |
|
10 |
8 9
|
lidlss |
|
11 |
7 10
|
syl |
|
12 |
11
|
ralrimiva |
|
13 |
|
unissb |
|
14 |
12 13
|
sylibr |
|
15 |
|
eqid |
|
16 |
15 8 9
|
rspcl |
|
17 |
3 14 16
|
syl2anc |
|
18 |
|
sseq1 |
|
19 |
18
|
rabbidv |
Could not format ( i = ( ( RSpan ` R ) ` U. r ) -> { j e. ( PrmIdeal ` R ) | i C_ j } = { j e. ( PrmIdeal ` R ) | ( ( RSpan ` R ) ` U. r ) C_ j } ) : No typesetting found for |- ( i = ( ( RSpan ` R ) ` U. r ) -> { j e. ( PrmIdeal ` R ) | i C_ j } = { j e. ( PrmIdeal ` R ) | ( ( RSpan ` R ) ` U. r ) C_ j } ) with typecode |- |
20 |
19
|
eqeq2d |
Could not format ( i = ( ( RSpan ` R ) ` U. r ) -> ( |^| S = { j e. ( PrmIdeal ` R ) | i C_ j } <-> |^| S = { j e. ( PrmIdeal ` R ) | ( ( RSpan ` R ) ` U. r ) C_ j } ) ) : No typesetting found for |- ( i = ( ( RSpan ` R ) ` U. r ) -> ( |^| S = { j e. ( PrmIdeal ` R ) | i C_ j } <-> |^| S = { j e. ( PrmIdeal ` R ) | ( ( RSpan ` R ) ` U. r ) C_ j } ) ) with typecode |- |
21 |
20
|
adantl |
Could not format ( ( ( ( ( ( R e. CRing /\ S C_ ran V ) /\ S =/= (/) ) /\ r e. ~P ( LIdeal ` R ) ) /\ S = ( V " r ) ) /\ i = ( ( RSpan ` R ) ` U. r ) ) -> ( |^| S = { j e. ( PrmIdeal ` R ) | i C_ j } <-> |^| S = { j e. ( PrmIdeal ` R ) | ( ( RSpan ` R ) ` U. r ) C_ j } ) ) : No typesetting found for |- ( ( ( ( ( ( R e. CRing /\ S C_ ran V ) /\ S =/= (/) ) /\ r e. ~P ( LIdeal ` R ) ) /\ S = ( V " r ) ) /\ i = ( ( RSpan ` R ) ` U. r ) ) -> ( |^| S = { j e. ( PrmIdeal ` R ) | i C_ j } <-> |^| S = { j e. ( PrmIdeal ` R ) | ( ( RSpan ` R ) ` U. r ) C_ j } ) ) with typecode |- |
22 |
|
simpr |
|
23 |
22
|
inteqd |
|
24 |
1
|
funmpt2 |
|
25 |
24
|
a1i |
|
26 |
|
fvex |
Could not format ( PrmIdeal ` R ) e. _V : No typesetting found for |- ( PrmIdeal ` R ) e. _V with typecode |- |
27 |
26
|
rabex |
Could not format { j e. ( PrmIdeal ` R ) | i C_ j } e. _V : No typesetting found for |- { j e. ( PrmIdeal ` R ) | i C_ j } e. _V with typecode |- |
28 |
27 1
|
dmmpti |
|
29 |
6 28
|
sseqtrrdi |
|
30 |
|
intimafv |
|
31 |
25 29 30
|
syl2anc |
|
32 |
23 31
|
eqtrd |
|
33 |
|
simplr |
|
34 |
|
simpr |
|
35 |
34
|
imaeq2d |
|
36 |
|
ima0 |
|
37 |
35 36
|
eqtrdi |
|
38 |
33 37
|
eqtrd |
|
39 |
|
simp-4r |
|
40 |
39
|
neneqd |
|
41 |
38 40
|
pm2.65da |
|
42 |
41
|
neqned |
|
43 |
1 15
|
zarclsiin |
|
44 |
3 6 42 43
|
syl3anc |
|
45 |
1
|
a1i |
Could not format ( ( ( ( ( R e. CRing /\ S C_ ran V ) /\ S =/= (/) ) /\ r e. ~P ( LIdeal ` R ) ) /\ S = ( V " r ) ) -> V = ( i e. ( LIdeal ` R ) |-> { j e. ( PrmIdeal ` R ) | i C_ j } ) ) : No typesetting found for |- ( ( ( ( ( R e. CRing /\ S C_ ran V ) /\ S =/= (/) ) /\ r e. ~P ( LIdeal ` R ) ) /\ S = ( V " r ) ) -> V = ( i e. ( LIdeal ` R ) |-> { j e. ( PrmIdeal ` R ) | i C_ j } ) ) with typecode |- |
46 |
19
|
adantl |
Could not format ( ( ( ( ( ( R e. CRing /\ S C_ ran V ) /\ S =/= (/) ) /\ r e. ~P ( LIdeal ` R ) ) /\ S = ( V " r ) ) /\ i = ( ( RSpan ` R ) ` U. r ) ) -> { j e. ( PrmIdeal ` R ) | i C_ j } = { j e. ( PrmIdeal ` R ) | ( ( RSpan ` R ) ` U. r ) C_ j } ) : No typesetting found for |- ( ( ( ( ( ( R e. CRing /\ S C_ ran V ) /\ S =/= (/) ) /\ r e. ~P ( LIdeal ` R ) ) /\ S = ( V " r ) ) /\ i = ( ( RSpan ` R ) ` U. r ) ) -> { j e. ( PrmIdeal ` R ) | i C_ j } = { j e. ( PrmIdeal ` R ) | ( ( RSpan ` R ) ` U. r ) C_ j } ) with typecode |- |
47 |
26
|
rabex |
Could not format { j e. ( PrmIdeal ` R ) | ( ( RSpan ` R ) ` U. r ) C_ j } e. _V : No typesetting found for |- { j e. ( PrmIdeal ` R ) | ( ( RSpan ` R ) ` U. r ) C_ j } e. _V with typecode |- |
48 |
47
|
a1i |
Could not format ( ( ( ( ( R e. CRing /\ S C_ ran V ) /\ S =/= (/) ) /\ r e. ~P ( LIdeal ` R ) ) /\ S = ( V " r ) ) -> { j e. ( PrmIdeal ` R ) | ( ( RSpan ` R ) ` U. r ) C_ j } e. _V ) : No typesetting found for |- ( ( ( ( ( R e. CRing /\ S C_ ran V ) /\ S =/= (/) ) /\ r e. ~P ( LIdeal ` R ) ) /\ S = ( V " r ) ) -> { j e. ( PrmIdeal ` R ) | ( ( RSpan ` R ) ` U. r ) C_ j } e. _V ) with typecode |- |
49 |
45 46 17 48
|
fvmptd |
Could not format ( ( ( ( ( R e. CRing /\ S C_ ran V ) /\ S =/= (/) ) /\ r e. ~P ( LIdeal ` R ) ) /\ S = ( V " r ) ) -> ( V ` ( ( RSpan ` R ) ` U. r ) ) = { j e. ( PrmIdeal ` R ) | ( ( RSpan ` R ) ` U. r ) C_ j } ) : No typesetting found for |- ( ( ( ( ( R e. CRing /\ S C_ ran V ) /\ S =/= (/) ) /\ r e. ~P ( LIdeal ` R ) ) /\ S = ( V " r ) ) -> ( V ` ( ( RSpan ` R ) ` U. r ) ) = { j e. ( PrmIdeal ` R ) | ( ( RSpan ` R ) ` U. r ) C_ j } ) with typecode |- |
50 |
32 44 49
|
3eqtrd |
Could not format ( ( ( ( ( R e. CRing /\ S C_ ran V ) /\ S =/= (/) ) /\ r e. ~P ( LIdeal ` R ) ) /\ S = ( V " r ) ) -> |^| S = { j e. ( PrmIdeal ` R ) | ( ( RSpan ` R ) ` U. r ) C_ j } ) : No typesetting found for |- ( ( ( ( ( R e. CRing /\ S C_ ran V ) /\ S =/= (/) ) /\ r e. ~P ( LIdeal ` R ) ) /\ S = ( V " r ) ) -> |^| S = { j e. ( PrmIdeal ` R ) | ( ( RSpan ` R ) ` U. r ) C_ j } ) with typecode |- |
51 |
17 21 50
|
rspcedvd |
Could not format ( ( ( ( ( R e. CRing /\ S C_ ran V ) /\ S =/= (/) ) /\ r e. ~P ( LIdeal ` R ) ) /\ S = ( V " r ) ) -> E. i e. ( LIdeal ` R ) |^| S = { j e. ( PrmIdeal ` R ) | i C_ j } ) : No typesetting found for |- ( ( ( ( ( R e. CRing /\ S C_ ran V ) /\ S =/= (/) ) /\ r e. ~P ( LIdeal ` R ) ) /\ S = ( V " r ) ) -> E. i e. ( LIdeal ` R ) |^| S = { j e. ( PrmIdeal ` R ) | i C_ j } ) with typecode |- |
52 |
|
intex |
|
53 |
52
|
biimpi |
|
54 |
53
|
3ad2ant3 |
|
55 |
1
|
elrnmpt |
Could not format ( |^| S e. _V -> ( |^| S e. ran V <-> E. i e. ( LIdeal ` R ) |^| S = { j e. ( PrmIdeal ` R ) | i C_ j } ) ) : No typesetting found for |- ( |^| S e. _V -> ( |^| S e. ran V <-> E. i e. ( LIdeal ` R ) |^| S = { j e. ( PrmIdeal ` R ) | i C_ j } ) ) with typecode |- |
56 |
54 55
|
syl |
Could not format ( ( R e. CRing /\ S C_ ran V /\ S =/= (/) ) -> ( |^| S e. ran V <-> E. i e. ( LIdeal ` R ) |^| S = { j e. ( PrmIdeal ` R ) | i C_ j } ) ) : No typesetting found for |- ( ( R e. CRing /\ S C_ ran V /\ S =/= (/) ) -> ( |^| S e. ran V <-> E. i e. ( LIdeal ` R ) |^| S = { j e. ( PrmIdeal ` R ) | i C_ j } ) ) with typecode |- |
57 |
56
|
ad5ant123 |
Could not format ( ( ( ( ( R e. CRing /\ S C_ ran V ) /\ S =/= (/) ) /\ r e. ~P ( LIdeal ` R ) ) /\ S = ( V " r ) ) -> ( |^| S e. ran V <-> E. i e. ( LIdeal ` R ) |^| S = { j e. ( PrmIdeal ` R ) | i C_ j } ) ) : No typesetting found for |- ( ( ( ( ( R e. CRing /\ S C_ ran V ) /\ S =/= (/) ) /\ r e. ~P ( LIdeal ` R ) ) /\ S = ( V " r ) ) -> ( |^| S e. ran V <-> E. i e. ( LIdeal ` R ) |^| S = { j e. ( PrmIdeal ` R ) | i C_ j } ) ) with typecode |- |
58 |
51 57
|
mpbird |
|
59 |
|
fvexd |
|
60 |
24
|
a1i |
|
61 |
|
simplr |
|
62 |
27 1
|
fnmpti |
|
63 |
|
fnima |
|
64 |
62 63
|
ax-mp |
|
65 |
61 64
|
sseqtrrdi |
|
66 |
|
ssimaexg |
|
67 |
59 60 65 66
|
syl3anc |
|
68 |
|
vex |
|
69 |
68
|
a1i |
|
70 |
|
simpr |
|
71 |
69 70
|
elpwd |
|
72 |
71
|
ex |
|
73 |
72
|
anim1d |
|
74 |
73
|
eximdv |
|
75 |
67 74
|
mpd |
|
76 |
|
df-rex |
|
77 |
75 76
|
sylibr |
|
78 |
58 77
|
r19.29a |
|
79 |
78
|
3impa |
|