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Metamath Proof Explorer

Theorem 0wdom

Description: Any set weakly dominates the empty set. (Contributed by Stefan O'Rear, 11-Feb-2015)

		Ref	Expression
	Assertion	0wdom	$⊢ X \in V \to \emptyset ≼^{*} X$

Step	Hyp	Ref	Expression
1		eqid	$⊢ \emptyset = \emptyset$
2	1	orci	$⊢ (\emptyset = \emptyset \lor \exists z z : X \underset{onto}{⟶} \emptyset)$
3		brwdom	$⊢ X \in V \to (\emptyset ≼^{*} X \leftrightarrow (\emptyset = \emptyset \lor \exists z z : X \underset{onto}{⟶} \emptyset))$
4	2 3	mpbiri	$⊢ X \in V \to \emptyset ≼^{*} X$