Theorem f1dm

Description: The domain of a one-to-one mapping. (Contributed by NM, 8-Mar-2014) (Proof shortened by Wolf Lammen, 29-May-2024)

	Ref	Expression
Assertion	f1dm	⊢ ( 𝐹 : 𝐴 –1-1→ 𝐵 → dom 𝐹 = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		f1fn	⊢ ( 𝐹 : 𝐴 –1-1→ 𝐵 → 𝐹 Fn 𝐴 )
2	1	fndmd	⊢ ( 𝐹 : 𝐴 –1-1→ 𝐵 → dom 𝐹 = 𝐴 )