Step |
Hyp |
Ref |
Expression |
1 |
|
isprmidlc.1 |
|
2 |
|
isprmidlc.2 |
|
3 |
|
simpr1 |
Could not format ( ( ( R e. CRing /\ P e. ( PrmIdeal ` R ) ) /\ ( I e. B /\ J e. B /\ ( I .x. J ) e. P ) ) -> I e. B ) : No typesetting found for |- ( ( ( R e. CRing /\ P e. ( PrmIdeal ` R ) ) /\ ( I e. B /\ J e. B /\ ( I .x. J ) e. P ) ) -> I e. B ) with typecode |- |
4 |
|
simpr2 |
Could not format ( ( ( R e. CRing /\ P e. ( PrmIdeal ` R ) ) /\ ( I e. B /\ J e. B /\ ( I .x. J ) e. P ) ) -> J e. B ) : No typesetting found for |- ( ( ( R e. CRing /\ P e. ( PrmIdeal ` R ) ) /\ ( I e. B /\ J e. B /\ ( I .x. J ) e. P ) ) -> J e. B ) with typecode |- |
5 |
1 2
|
isprmidlc |
Could not format ( R e. CRing -> ( P e. ( PrmIdeal ` R ) <-> ( P e. ( LIdeal ` R ) /\ P =/= B /\ A. a e. B A. b e. B ( ( a .x. b ) e. P -> ( a e. P \/ b e. P ) ) ) ) ) : No typesetting found for |- ( R e. CRing -> ( P e. ( PrmIdeal ` R ) <-> ( P e. ( LIdeal ` R ) /\ P =/= B /\ A. a e. B A. b e. B ( ( a .x. b ) e. P -> ( a e. P \/ b e. P ) ) ) ) ) with typecode |- |
6 |
5
|
biimpa |
Could not format ( ( R e. CRing /\ P e. ( PrmIdeal ` R ) ) -> ( P e. ( LIdeal ` R ) /\ P =/= B /\ A. a e. B A. b e. B ( ( a .x. b ) e. P -> ( a e. P \/ b e. P ) ) ) ) : No typesetting found for |- ( ( R e. CRing /\ P e. ( PrmIdeal ` R ) ) -> ( P e. ( LIdeal ` R ) /\ P =/= B /\ A. a e. B A. b e. B ( ( a .x. b ) e. P -> ( a e. P \/ b e. P ) ) ) ) with typecode |- |
7 |
6
|
simp3d |
Could not format ( ( R e. CRing /\ P e. ( PrmIdeal ` R ) ) -> A. a e. B A. b e. B ( ( a .x. b ) e. P -> ( a e. P \/ b e. P ) ) ) : No typesetting found for |- ( ( R e. CRing /\ P e. ( PrmIdeal ` R ) ) -> A. a e. B A. b e. B ( ( a .x. b ) e. P -> ( a e. P \/ b e. P ) ) ) with typecode |- |
8 |
7
|
adantr |
Could not format ( ( ( R e. CRing /\ P e. ( PrmIdeal ` R ) ) /\ ( I e. B /\ J e. B /\ ( I .x. J ) e. P ) ) -> A. a e. B A. b e. B ( ( a .x. b ) e. P -> ( a e. P \/ b e. P ) ) ) : No typesetting found for |- ( ( ( R e. CRing /\ P e. ( PrmIdeal ` R ) ) /\ ( I e. B /\ J e. B /\ ( I .x. J ) e. P ) ) -> A. a e. B A. b e. B ( ( a .x. b ) e. P -> ( a e. P \/ b e. P ) ) ) with typecode |- |
9 |
|
simpr3 |
Could not format ( ( ( R e. CRing /\ P e. ( PrmIdeal ` R ) ) /\ ( I e. B /\ J e. B /\ ( I .x. J ) e. P ) ) -> ( I .x. J ) e. P ) : No typesetting found for |- ( ( ( R e. CRing /\ P e. ( PrmIdeal ` R ) ) /\ ( I e. B /\ J e. B /\ ( I .x. J ) e. P ) ) -> ( I .x. J ) e. P ) with typecode |- |
10 |
|
oveq12 |
|
11 |
10
|
eleq1d |
|
12 |
|
simpl |
|
13 |
12
|
eleq1d |
|
14 |
|
simpr |
|
15 |
14
|
eleq1d |
|
16 |
13 15
|
orbi12d |
|
17 |
11 16
|
imbi12d |
|
18 |
17
|
rspc2gv |
|
19 |
18
|
imp31 |
|
20 |
3 4 8 9 19
|
syl1111anc |
Could not format ( ( ( R e. CRing /\ P e. ( PrmIdeal ` R ) ) /\ ( I e. B /\ J e. B /\ ( I .x. J ) e. P ) ) -> ( I e. P \/ J e. P ) ) : No typesetting found for |- ( ( ( R e. CRing /\ P e. ( PrmIdeal ` R ) ) /\ ( I e. B /\ J e. B /\ ( I .x. J ) e. P ) ) -> ( I e. P \/ J e. P ) ) with typecode |- |