Description: A strict order relation has no 3-cycle loops. (Contributed by NM, 21-Jan-1996)
Ref | Expression | ||
---|---|---|---|
Assertion | so3nr | |- ( ( R Or A /\ ( B e. A /\ C e. A /\ D e. A ) ) -> -. ( B R C /\ C R D /\ D R B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sopo | |- ( R Or A -> R Po A ) |
|
2 | po3nr | |- ( ( R Po A /\ ( B e. A /\ C e. A /\ D e. A ) ) -> -. ( B R C /\ C R D /\ D R B ) ) |
|
3 | 1 2 | sylan | |- ( ( R Or A /\ ( B e. A /\ C e. A /\ D e. A ) ) -> -. ( B R C /\ C R D /\ D R B ) ) |