Theorem f1orel 5149

Description: A one-to-one onto mapping is a relation. (Contributed by NM, 13-Dec-2003.)

Assertion

Ref	Expression
f1orel	⊢ (𝐹:𝐴–1-1-onto→𝐵 → Rel 𝐹)

Proof of Theorem f1orel

Step	Hyp	Ref	Expression
1		f1ofun 5148	. 2 ⊢ (𝐹:𝐴–1-1-onto→𝐵 → Fun 𝐹)
2		funrel 4939	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 14	1 ⊢ (𝐹:𝐴–1-1-onto→𝐵 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 4368  Fun wfun 4916  –1-1-onto→wf1o 4921

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104

This theorem depends on definitions:  df-bi 115  df-fun 4924  df-fn 4925  df-f 4926  df-f1 4927  df-f1o 4929

This theorem is referenced by:  f1ococnv1  5175  isores1  5474  dif1en  6364