ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  dffn4 GIF version

Theorem dffn4 5321
Description: A function maps onto its range. (Contributed by NM, 10-May-1998.)
Assertion
Ref Expression
dffn4 (𝐹 Fn 𝐴𝐹:𝐴onto→ran 𝐹)

Proof of Theorem dffn4
StepHypRef Expression
1 eqid 2117 . . 3 ran 𝐹 = ran 𝐹
21biantru 300 . 2 (𝐹 Fn 𝐴 ↔ (𝐹 Fn 𝐴 ∧ ran 𝐹 = ran 𝐹))
3 df-fo 5099 . 2 (𝐹:𝐴onto→ran 𝐹 ↔ (𝐹 Fn 𝐴 ∧ ran 𝐹 = ran 𝐹))
42, 3bitr4i 186 1 (𝐹 Fn 𝐴𝐹:𝐴onto→ran 𝐹)
Colors of variables: wff set class
Syntax hints:  wa 103  wb 104   = wceq 1316  ran crn 4510   Fn wfn 5088  ontowfo 5091
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1410  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-cleq 2110  df-fo 5099
This theorem is referenced by:  funforn  5322  ffoss  5367  tposf2  6133  mapsn  6552  fifo  6836
  Copyright terms: Public domain W3C validator