Theorem f1rel 5095

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 5093	. 2 ⊢ (𝐹:𝐴–1-1→𝐵 → 𝐹 Fn 𝐴)
2		fnrel 4997	. 2 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)
3	1, 2	syl 14	1 ⊢ (𝐹:𝐴–1-1→𝐵 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 4350   Fn wfn 4897  –1-1→wf1 4899

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99

This theorem depends on definitions:  df-bi 110  df-fun 4904  df-fn 4905  df-f 4906  df-f1 4907

This theorem is referenced by: (None)