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Metamath Proof Explorer

Theorem freld

Description: A mapping is a relation. (Contributed by Glauco Siliprandi, 26-Jun-2021)

Ref Expression
Hypothesis freld.1 ⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐵 )
Assertion freld ( 𝜑 → Rel 𝐹 )

Proof

Step Hyp Ref Expression
1 freld.1 ⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐵 )
2 frel ⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → Rel 𝐹 )
3 1 2 syl ⊢ ( 𝜑 → Rel 𝐹 )