Step |
Hyp |
Ref |
Expression |
1 |
|
poirr |
|- ( ( R Po A /\ X e. A ) -> -. X R X ) |
2 |
|
elpredg |
|- ( ( X e. A /\ X e. A ) -> ( X e. Pred ( R , A , X ) <-> X R X ) ) |
3 |
2
|
anidms |
|- ( X e. A -> ( X e. Pred ( R , A , X ) <-> X R X ) ) |
4 |
3
|
notbid |
|- ( X e. A -> ( -. X e. Pred ( R , A , X ) <-> -. X R X ) ) |
5 |
1 4
|
syl5ibr |
|- ( X e. A -> ( ( R Po A /\ X e. A ) -> -. X e. Pred ( R , A , X ) ) ) |
6 |
5
|
expd |
|- ( X e. A -> ( R Po A -> ( X e. A -> -. X e. Pred ( R , A , X ) ) ) ) |
7 |
6
|
pm2.43b |
|- ( R Po A -> ( X e. A -> -. X e. Pred ( R , A , X ) ) ) |
8 |
|
predel |
|- ( X e. Pred ( R , A , X ) -> X e. A ) |
9 |
8
|
con3i |
|- ( -. X e. A -> -. X e. Pred ( R , A , X ) ) |
10 |
7 9
|
pm2.61d1 |
|- ( R Po A -> -. X e. Pred ( R , A , X ) ) |