Theorem forn

Description: The codomain of an onto function is its range. (Contributed by NM, 3-Aug-1994)

	Ref	Expression
Assertion	forn	⊢ ( 𝐹 : 𝐴 –onto→ 𝐵 → ran 𝐹 = 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		df-fo	⊢ ( 𝐹 : 𝐴 –onto→ 𝐵 ↔ ( 𝐹 Fn 𝐴 ∧ ran 𝐹 = 𝐵 ) )
2	1	simprbi	⊢ ( 𝐹 : 𝐴 –onto→ 𝐵 → ran 𝐹 = 𝐵 )