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Metamath Proof Explorer

Theorem fndmu

Description: A function has a unique domain. (Contributed by NM, 11-Aug-1994)

Ref Expression
Assertion fndmu ( ( 𝐹 Fn 𝐴 ∧ 𝐹 Fn 𝐵 ) → 𝐴 = 𝐵 )

Proof

Step Hyp Ref Expression
1 fndm ⊢ ( 𝐹 Fn 𝐴 → dom 𝐹 = 𝐴 )
2 fndm ⊢ ( 𝐹 Fn 𝐵 → dom 𝐹 = 𝐵 )
3 1 2 sylan9req ⊢ ( ( 𝐹 Fn 𝐴 ∧ 𝐹 Fn 𝐵 ) → 𝐴 = 𝐵 )