Theorem f1orel 5642

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 5641	. 2 ⊢ (𝐹:𝐴–1-1-onto→𝐵 → Fun 𝐹)
2		funrel 5394	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 14	1 ⊢ (𝐹:𝐴–1-1-onto→𝐵 → Rel 𝐹)

This proof depends on syntax axioms:   → wi 4  Rel wrel 4779  Fun wfun 5371  –1-1-onto→wf1o 5376

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106

This proof depends on definitions:  df-bi 117  df-fun 5379  df-fn 5380  df-f 5381  df-f1 5382  df-f1o 5384

This theorem is used by:  f1ococnv1  5668  isores1  6020  ssenen  7152  dif1en  7183