Theorem frel 5408

Description: A mapping is a relation. (Contributed by NM, 3-Aug-1994.)

Assertion

Ref	Expression
frel	⊢ (𝐹:𝐴⟶𝐵 → Rel 𝐹)

Proof of Theorem frel

Step	Hyp	Ref	Expression
1		ffn 5403	. 2 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹 Fn 𝐴)
2		fnrel 5352	. 2 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)
3	1, 2	syl 14	1 ⊢ (𝐹:𝐴⟶𝐵 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 4664   Fn wfn 5249  ⟶wf 5250

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106

This theorem depends on definitions:  df-bi 117  df-fun 5256  df-fn 5257  df-f 5258

This theorem is referenced by:  fssxp  5421  fsn  5730  eluzel2  9597  hmeocnv  14475  metn0  14546