Theorem brdom

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

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

Proof

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