NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  f1fn GIF version

Theorem f1fn 5259
Description: A one-to-one mapping is a function on its domain. (Contributed by set.mm contributors, 8-Mar-2014.)
Assertion
Ref Expression
f1fn (F:A1-1BF Fn A)

Proof of Theorem f1fn
StepHypRef Expression
1 f1f 5258 . 2 (F:A1-1BF:A–→B)
2 ffn 5223 . 2 (F:A–→BF Fn A)
31, 2syl 15 1 (F:A1-1BF Fn A)
Colors of variables: wff setvar class
Syntax hints:  wi 4   Fn wfn 4776  –→wf 4777  1-1wf1 4778
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 177  df-an 360  df-f 4791  df-f1 4792
This theorem is referenced by:  f1fun  5260  f1dm  5261  f1f1orn  5297  f1elima  5474
  Copyright terms: Public domain W3C validator