This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem ordtr1

Description: Transitive law for ordinal classes. (Contributed by NM, 12-Dec-2004)

		Ref	Expression
	Assertion	ordtr1	$⊢ Ord C \to ((A \in B \land B \in C) \to A \in C)$

Step	Hyp	Ref	Expression
1		ordtr	$⊢ Ord C \to Tr C$
2		trel	$⊢ Tr C \to ((A \in B \land B \in C) \to A \in C)$
3	1 2	syl	$⊢ Ord C \to ((A \in B \land B \in C) \to A \in C)$