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Metamath Proof Explorer

Theorem fndmi

Description: The domain of a function. (Contributed by Wolf Lammen, 1-Jun-2024)

Ref Expression
Hypothesis fndmi.1 ⊢ 𝐹 Fn 𝐴
Assertion fndmi dom 𝐹 = 𝐴

Proof

Step Hyp Ref Expression
1 fndmi.1 ⊢ 𝐹 Fn 𝐴
2 fndm ⊢ ( 𝐹 Fn 𝐴 → dom 𝐹 = 𝐴 )
3 1 2 ax-mp ⊢ dom 𝐹 = 𝐴