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	$$⊢B\in \mathrm{V}$$
Assertion	f1dom	$$⊢F:A\underset{1-1}{⟶}B\to A\preccurlyeq B$$

Proof

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