Theorem freld 6746

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 6745	. 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 5663  ⟶wf 6562

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 6568  df-fn 6569  df-f 6570

This theorem is used by:  f1rel  6812  focofo  6839  1arithidom  34173  esplyind  34318  evlselvlem  43882  f1cof1blem  48417  funfocofob  48421