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Metamath Proof Explorer

Theorem so2nr

Description: A strict order relation has no 2-cycle loops. (Contributed by NM, 21-Jan-1996)

		Ref	Expression
	Assertion	so2nr	$⊢ (R Or A \land (B \in A \land C \in A)) \to \neg (B R C \land C R B)$

Step	Hyp	Ref	Expression
1		sopo	$⊢ R Or A \to R Po A$
2		po2nr	$⊢ (R Po A \land (B \in A \land C \in A)) \to \neg (B R C \land C R B)$
3	1 2	sylan	$⊢ (R Or A \land (B \in A \land C \in A)) \to \neg (B R C \land C R B)$