Theorem fdm

Description: The domain of a mapping. (Contributed by NM, 2-Aug-1994) (Proof shortened by Wolf Lammen, 29-May-2024)

	Ref	Expression
Assertion	fdm	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → dom 𝐹 = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		ffn	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → 𝐹 Fn 𝐴 )
2	1	fndmd	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → dom 𝐹 = 𝐴 )