ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  f1rel GIF version

Theorem f1rel 5380
Description: A one-to-one onto mapping is a relation. (Contributed by NM, 8-Mar-2014.)
Assertion
Ref Expression
f1rel (𝐹:𝐴1-1𝐵 → Rel 𝐹)

Proof of Theorem f1rel
StepHypRef Expression
1 f1fn 5378 . 2 (𝐹:𝐴1-1𝐵𝐹 Fn 𝐴)
2 fnrel 5269 . 2 (𝐹 Fn 𝐴 → Rel 𝐹)
31, 2syl 14 1 (𝐹:𝐴1-1𝐵 → Rel 𝐹)
Colors of variables: wff set class
Syntax hints:  wi 4  Rel wrel 4592   Fn wfn 5166  1-1wf1 5168
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105
This theorem depends on definitions:  df-bi 116  df-fun 5173  df-fn 5174  df-f 5175  df-f1 5176
This theorem is referenced by:  f1dmvrnfibi  6889
  Copyright terms: Public domain W3C validator