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Metamath Proof Explorer

Theorem sonr

Description: A strict order relation is irreflexive. (Contributed by NM, 24-Nov-1995)

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

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