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

Metamath Proof Explorer

Theorem we0

Description: Any relation is a well-ordering of the empty set. (Contributed by NM, 16-Mar-1997)

		Ref	Expression
	Assertion	we0	$⊢ R We \emptyset$

Step	Hyp	Ref	Expression
1		fr0	$⊢ R Fr \emptyset$
2		so0	$⊢ R Or \emptyset$
3		df-we	$⊢ R We \emptyset \leftrightarrow (R Fr \emptyset \land R Or \emptyset)$
4	1 2 3	mpbir2an	$⊢ R We \emptyset$