Theorem f1rel 6673

Description: A one-to-one onto mapping is a relation. (Contributed by NM, 8-Mar-2014.)

Assertion

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

Proof of Theorem f1rel

Step	Hyp	Ref	Expression
1		f1fn 6671	. 2 ⊢ (𝐹:𝐴–1-1→𝐵 → 𝐹 Fn 𝐴)
2		fnrel 6535	. 2 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹:𝐴–1-1→𝐵 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5594   Fn wfn 6428  –1-1→wf1 6430

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 206  df-an 397  df-fun 6435  df-fn 6436  df-f 6437  df-f1 6438

This theorem is referenced by:  f1domfi  8967