Theorem freld 6710

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 6709	. 2 ⊢ (𝐹:𝐴⟶𝐵 → Rel 𝐹)
3	1, 2	syl 18	1 ⊢ (𝜑 → Rel 𝐹)

This proof depends on syntax axioms:   → wi 4  Rel wrel 5660  ⟶wf 6529

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-fun 6535  df-fn 6536  df-f 6537

This theorem is used by:  f1rel  6776  focofo  6803  1arithidom  33948  esplyind  34086  evlselvlem  43435  f1cof1blem  47963  funfocofob  47967