Theorem f1of

Description: A one-to-one onto mapping is a mapping. (Contributed by NM, 12-Dec-2003)

	Ref	Expression
Assertion	f1of	$$⊢F:A\underset{1-1\; onto}{⟶}B\to F:A⟶B$$

Proof

Step	Hyp	Ref	Expression
1		f1of1	$$⊢F:A\underset{1-1\; onto}{⟶}B\to F:A\underset{1-1}{⟶}B$$
2		f1f	$$⊢F:A\underset{1-1}{⟶}B\to F:A⟶B$$
3	1 2	syl	$$⊢F:A\underset{1-1\; onto}{⟶}B\to F:A⟶B$$