Step |
Hyp |
Ref |
Expression |
1 |
|
ssmxidl.1 |
|
2 |
|
neeq1 |
|
3 |
|
sseq2 |
|
4 |
2 3
|
anbi12d |
|
5 |
|
simp2 |
|
6 |
|
simp3 |
|
7 |
|
ssidd |
|
8 |
6 7
|
jca |
|
9 |
4 5 8
|
elrabd |
|
10 |
9
|
ne0d |
|
11 |
|
eqid |
|
12 |
|
simpl1 |
|
13 |
|
simpl2 |
|
14 |
|
simpl3 |
|
15 |
|
simpr1 |
|
16 |
|
simpr2 |
|
17 |
|
simpr3 |
|
18 |
1 11 12 13 14 15 16 17
|
ssmxidllem |
|
19 |
18
|
ex |
|
20 |
19
|
alrimiv |
|
21 |
|
fvex |
|
22 |
21
|
rabex |
|
23 |
22
|
zornn0 |
|
24 |
10 20 23
|
syl2anc |
|
25 |
|
neeq1 |
|
26 |
|
sseq2 |
|
27 |
25 26
|
anbi12d |
|
28 |
27
|
elrab |
|
29 |
28
|
anbi2i |
|
30 |
|
simpll1 |
|
31 |
|
simplrl |
|
32 |
|
simplr |
|
33 |
32
|
simprld |
|
34 |
|
psseq2 |
|
35 |
34
|
notbid |
|
36 |
|
simp-4r |
|
37 |
|
neeq1 |
|
38 |
|
sseq2 |
|
39 |
37 38
|
anbi12d |
|
40 |
|
simpllr |
|
41 |
|
simpr |
|
42 |
41
|
neqned |
|
43 |
|
simp-5r |
|
44 |
43
|
simprrd |
|
45 |
|
simplr |
|
46 |
44 45
|
sstrd |
|
47 |
42 46
|
jca |
|
48 |
39 40 47
|
elrabd |
|
49 |
35 36 48
|
rspcdva |
|
50 |
|
npss |
|
51 |
50
|
biimpi |
|
52 |
49 45 51
|
sylc |
|
53 |
52
|
equcomd |
|
54 |
53
|
ex |
|
55 |
54
|
orrd |
|
56 |
55
|
orcomd |
|
57 |
56
|
ex |
|
58 |
57
|
ralrimiva |
|
59 |
1
|
ismxidl |
Could not format ( R e. Ring -> ( m e. ( MaxIdeal ` R ) <-> ( m e. ( LIdeal ` R ) /\ m =/= B /\ A. k e. ( LIdeal ` R ) ( m C_ k -> ( k = m \/ k = B ) ) ) ) ) : No typesetting found for |- ( R e. Ring -> ( m e. ( MaxIdeal ` R ) <-> ( m e. ( LIdeal ` R ) /\ m =/= B /\ A. k e. ( LIdeal ` R ) ( m C_ k -> ( k = m \/ k = B ) ) ) ) ) with typecode |- |
60 |
59
|
biimpar |
Could not format ( ( R e. Ring /\ ( m e. ( LIdeal ` R ) /\ m =/= B /\ A. k e. ( LIdeal ` R ) ( m C_ k -> ( k = m \/ k = B ) ) ) ) -> m e. ( MaxIdeal ` R ) ) : No typesetting found for |- ( ( R e. Ring /\ ( m e. ( LIdeal ` R ) /\ m =/= B /\ A. k e. ( LIdeal ` R ) ( m C_ k -> ( k = m \/ k = B ) ) ) ) -> m e. ( MaxIdeal ` R ) ) with typecode |- |
61 |
30 31 33 58 60
|
syl13anc |
Could not format ( ( ( ( R e. Ring /\ I e. ( LIdeal ` R ) /\ I =/= B ) /\ ( m e. ( LIdeal ` R ) /\ ( m =/= B /\ I C_ m ) ) ) /\ A. j e. { p e. ( LIdeal ` R ) | ( p =/= B /\ I C_ p ) } -. m C. j ) -> m e. ( MaxIdeal ` R ) ) : No typesetting found for |- ( ( ( ( R e. Ring /\ I e. ( LIdeal ` R ) /\ I =/= B ) /\ ( m e. ( LIdeal ` R ) /\ ( m =/= B /\ I C_ m ) ) ) /\ A. j e. { p e. ( LIdeal ` R ) | ( p =/= B /\ I C_ p ) } -. m C. j ) -> m e. ( MaxIdeal ` R ) ) with typecode |- |
62 |
32
|
simprrd |
|
63 |
61 62
|
jca |
Could not format ( ( ( ( R e. Ring /\ I e. ( LIdeal ` R ) /\ I =/= B ) /\ ( m e. ( LIdeal ` R ) /\ ( m =/= B /\ I C_ m ) ) ) /\ A. j e. { p e. ( LIdeal ` R ) | ( p =/= B /\ I C_ p ) } -. m C. j ) -> ( m e. ( MaxIdeal ` R ) /\ I C_ m ) ) : No typesetting found for |- ( ( ( ( R e. Ring /\ I e. ( LIdeal ` R ) /\ I =/= B ) /\ ( m e. ( LIdeal ` R ) /\ ( m =/= B /\ I C_ m ) ) ) /\ A. j e. { p e. ( LIdeal ` R ) | ( p =/= B /\ I C_ p ) } -. m C. j ) -> ( m e. ( MaxIdeal ` R ) /\ I C_ m ) ) with typecode |- |
64 |
29 63
|
sylanb |
Could not format ( ( ( ( R e. Ring /\ I e. ( LIdeal ` R ) /\ I =/= B ) /\ m e. { p e. ( LIdeal ` R ) | ( p =/= B /\ I C_ p ) } ) /\ A. j e. { p e. ( LIdeal ` R ) | ( p =/= B /\ I C_ p ) } -. m C. j ) -> ( m e. ( MaxIdeal ` R ) /\ I C_ m ) ) : No typesetting found for |- ( ( ( ( R e. Ring /\ I e. ( LIdeal ` R ) /\ I =/= B ) /\ m e. { p e. ( LIdeal ` R ) | ( p =/= B /\ I C_ p ) } ) /\ A. j e. { p e. ( LIdeal ` R ) | ( p =/= B /\ I C_ p ) } -. m C. j ) -> ( m e. ( MaxIdeal ` R ) /\ I C_ m ) ) with typecode |- |
65 |
64
|
expl |
Could not format ( ( R e. Ring /\ I e. ( LIdeal ` R ) /\ I =/= B ) -> ( ( m e. { p e. ( LIdeal ` R ) | ( p =/= B /\ I C_ p ) } /\ A. j e. { p e. ( LIdeal ` R ) | ( p =/= B /\ I C_ p ) } -. m C. j ) -> ( m e. ( MaxIdeal ` R ) /\ I C_ m ) ) ) : No typesetting found for |- ( ( R e. Ring /\ I e. ( LIdeal ` R ) /\ I =/= B ) -> ( ( m e. { p e. ( LIdeal ` R ) | ( p =/= B /\ I C_ p ) } /\ A. j e. { p e. ( LIdeal ` R ) | ( p =/= B /\ I C_ p ) } -. m C. j ) -> ( m e. ( MaxIdeal ` R ) /\ I C_ m ) ) ) with typecode |- |
66 |
65
|
reximdv2 |
Could not format ( ( R e. Ring /\ I e. ( LIdeal ` R ) /\ I =/= B ) -> ( E. m e. { p e. ( LIdeal ` R ) | ( p =/= B /\ I C_ p ) } A. j e. { p e. ( LIdeal ` R ) | ( p =/= B /\ I C_ p ) } -. m C. j -> E. m e. ( MaxIdeal ` R ) I C_ m ) ) : No typesetting found for |- ( ( R e. Ring /\ I e. ( LIdeal ` R ) /\ I =/= B ) -> ( E. m e. { p e. ( LIdeal ` R ) | ( p =/= B /\ I C_ p ) } A. j e. { p e. ( LIdeal ` R ) | ( p =/= B /\ I C_ p ) } -. m C. j -> E. m e. ( MaxIdeal ` R ) I C_ m ) ) with typecode |- |
67 |
24 66
|
mpd |
Could not format ( ( R e. Ring /\ I e. ( LIdeal ` R ) /\ I =/= B ) -> E. m e. ( MaxIdeal ` R ) I C_ m ) : No typesetting found for |- ( ( R e. Ring /\ I e. ( LIdeal ` R ) /\ I =/= B ) -> E. m e. ( MaxIdeal ` R ) I C_ m ) with typecode |- |