Theorem f1odm

Description: The domain of a one-to-one onto mapping. (Contributed by NM, 8-Mar-2014)

	Ref	Expression
Assertion	f1odm	⊢ ( 𝐹 : 𝐴 –1-1-onto→ 𝐵 → dom 𝐹 = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		f1ofn	⊢ ( 𝐹 : 𝐴 –1-1-onto→ 𝐵 → 𝐹 Fn 𝐴 )
2		fndm	⊢ ( 𝐹 Fn 𝐴 → dom 𝐹 = 𝐴 )
3	1 2	syl	⊢ ( 𝐹 : 𝐴 –1-1-onto→ 𝐵 → dom 𝐹 = 𝐴 )