Step |
Hyp |
Ref |
Expression |
1 |
|
poirr |
|- ( ( R Po A /\ B e. A ) -> -. B R B ) |
2 |
1
|
adantrr |
|- ( ( R Po A /\ ( B e. A /\ C e. A ) ) -> -. B R B ) |
3 |
|
potr |
|- ( ( R Po A /\ ( B e. A /\ C e. A /\ B e. A ) ) -> ( ( B R C /\ C R B ) -> B R B ) ) |
4 |
3
|
3exp2 |
|- ( R Po A -> ( B e. A -> ( C e. A -> ( B e. A -> ( ( B R C /\ C R B ) -> B R B ) ) ) ) ) |
5 |
4
|
com34 |
|- ( R Po A -> ( B e. A -> ( B e. A -> ( C e. A -> ( ( B R C /\ C R B ) -> B R B ) ) ) ) ) |
6 |
5
|
pm2.43d |
|- ( R Po A -> ( B e. A -> ( C e. A -> ( ( B R C /\ C R B ) -> B R B ) ) ) ) |
7 |
6
|
imp32 |
|- ( ( R Po A /\ ( B e. A /\ C e. A ) ) -> ( ( B R C /\ C R B ) -> B R B ) ) |
8 |
2 7
|
mtod |
|- ( ( R Po A /\ ( B e. A /\ C e. A ) ) -> -. ( B R C /\ C R B ) ) |