Theorem freld 6713

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 6712	. 2 ⊢ (𝐹:𝐴⟶𝐵 → Rel 𝐹)
3	1, 2	syl 18	1 ⊢ (𝜑 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5667  ⟶wf 6533

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 210  df-an 401  df-fun 6539  df-fn 6540  df-f 6541

This theorem is referenced by:  f1rel  6779  focofo  6806  1arithidom  33772  esplyind  33910  evlselvlem  43212  f1cof1blem  47700  funfocofob  47704