Theorem f1ofo

Description: A one-to-one onto function is an onto function. (Contributed by NM, 28-Apr-2004)

	Ref	Expression
Assertion	f1ofo	⊢ ( 𝐹 : 𝐴 –1-1-onto→ 𝐵 → 𝐹 : 𝐴 –onto→ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		dff1o3	⊢ ( 𝐹 : 𝐴 –1-1-onto→ 𝐵 ↔ ( 𝐹 : 𝐴 –onto→ 𝐵 ∧ Fun ◡ 𝐹 ) )
2	1	simplbi	⊢ ( 𝐹 : 𝐴 –1-1-onto→ 𝐵 → 𝐹 : 𝐴 –onto→ 𝐵 )