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Metamath Proof Explorer

Theorem 0lt1o

Description: Ordinal zero is less than ordinal one. (Contributed by NM, 5-Jan-2005)

		Ref	Expression
	Assertion	0lt1o	$⊢ \emptyset \in 1_{𝑜}$

Step	Hyp	Ref	Expression
1		eqid	$⊢ \emptyset = \emptyset$
2		el1o	$⊢ \emptyset \in 1_{𝑜} \leftrightarrow \emptyset = \emptyset$
3	1 2	mpbir	$⊢ \emptyset \in 1_{𝑜}$