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Metamath Proof Explorer

Theorem brdom

Description: Dominance relation. (Contributed by NM, 15-Jun-1998)

		Ref	Expression
	Hypothesis	bren.1	$⊢ B \in V$
	Assertion	brdom	$⊢ A ≼ B \leftrightarrow \exists f f : A \underset{1-1}{⟶} B$

Step	Hyp	Ref	Expression
1		bren.1	$⊢ B \in V$
2		brdomg	$⊢ B \in V \to (A ≼ B \leftrightarrow \exists f f : A \underset{1-1}{⟶} B)$
3	1 2	ax-mp	$⊢ A ≼ B \leftrightarrow \exists f f : A \underset{1-1}{⟶} B$