Metamath Proof Explorer


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