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Metamath Proof Explorer

Theorem f1dom

Description: The domain of a one-to-one function is dominated by its codomain. (Contributed by NM, 19-Jun-1998)

		Ref	Expression
	Hypothesis	f1dom.1	$⊢ B \in V$
	Assertion	f1dom	$⊢ F : A \underset{1-1}{⟶} B \to A ≼ B$

Step	Hyp	Ref	Expression
1		f1dom.1	$⊢ B \in V$
2		f1domg	$⊢ B \in V \to (F : A \underset{1-1}{⟶} B \to A ≼ B)$
3	1 2	ax-mp	$⊢ F : A \underset{1-1}{⟶} B \to A ≼ B$