Theorem f1rel 6782

Description: A one-to-one onto mapping is a relation. (Contributed by NM, 8-Mar-2014.) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026.)

Assertion

Ref	Expression
f1rel	⊢ (𝐹:𝐴–1-1→𝐵 → Rel 𝐹)

Proof of Theorem f1rel

Step	Hyp	Ref	Expression
1		f1f 6778	. 2 ⊢ (𝐹:𝐴–1-1→𝐵 → 𝐹:𝐴⟶𝐵)
2	1	freld 6716	1 ⊢ (𝐹:𝐴–1-1→𝐵 → Rel 𝐹)

This proof depends on syntax axioms:   → wi 4  Rel wrel 5655  –1-1→wf1 6535

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 6540  df-fn 6541  df-f 6542  df-f1 6543

This theorem is used by:  f1domfi  9196