Theorem f1of1

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

	Ref	Expression
Assertion	f1of1	$$⊢F:A\underset{1-1\; onto}{⟶}B\to F:A\underset{1-1}{⟶}B$$

Proof

Step	Hyp	Ref	Expression
1		df-f1o	$$⊢F:A\underset{1-1\; onto}{⟶}B\leftrightarrow \left(F:A\underset{1-1}{⟶}B\wedge F:A\underset{onto}{⟶}B\right)$$
2	1	simplbi	$$⊢F:A\underset{1-1\; onto}{⟶}B\to F:A\underset{1-1}{⟶}B$$