Theorem sotr

Description: A strict order relation is a transitive relation. (Contributed by NM, 21-Jan-1996)

	Ref	Expression
Assertion	sotr	|- ( ( R Or A /\ ( B e. A /\ C e. A /\ D e. A ) ) -> ( ( B R C /\ C R D ) -> B R D ) )

Proof

Step	Hyp	Ref	Expression
1		sopo	|- ( R Or A -> R Po A )
2		potr	|- ( ( R Po A /\ ( B e. A /\ C e. A /\ D e. A ) ) -> ( ( B R C /\ C R D ) -> B R D ) )
3	1 2	sylan	|- ( ( R Or A /\ ( B e. A /\ C e. A /\ D e. A ) ) -> ( ( B R C /\ C R D ) -> B R D ) )