Theorem freld 38420

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

Hypothesis

Ref	Expression
freld.1	⊢ (𝜑 → 𝐹:𝐴⟶𝐵)

Assertion

Ref	Expression
freld	⊢ (𝜑 → Rel 𝐹)

Proof of Theorem freld

Step	Hyp	Ref	Expression
1		freld.1	. 2 ⊢ (𝜑 → 𝐹:𝐴⟶𝐵)
2		frel 5963	. 2 ⊢ (𝐹:𝐴⟶𝐵 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝜑 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5043  ⟶wf 5800

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 196  df-an 385  df-fun 5806  df-fn 5807  df-f 5808

This theorem is referenced by:  sssmf  39625