Theorem fdmi

Description: Inference associated with fdm . The domain of a mapping. (Contributed by NM, 28-Jul-2008)

	Ref	Expression
Hypothesis	fdmi.1	⊢ 𝐹 : 𝐴 ⟶ 𝐵
Assertion	fdmi	⊢ dom 𝐹 = 𝐴

Proof

Step	Hyp	Ref	Expression
1		fdmi.1	⊢ 𝐹 : 𝐴 ⟶ 𝐵
2		fdm	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → dom 𝐹 = 𝐴 )
3	1 2	ax-mp	⊢ dom 𝐹 = 𝐴