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Theorem dffn2 5098
Description: Any function is a mapping into V. (Contributed by NM, 31-Oct-1995.) (Proof shortened by Andrew Salmon, 17-Sep-2011.)
Assertion
Ref Expression
dffn2 (𝐹 Fn 𝐴𝐹:𝐴⟶V)

Proof of Theorem dffn2
StepHypRef Expression
1 ssv 3028 . . 3 ran 𝐹 ⊆ V
21biantru 296 . 2 (𝐹 Fn 𝐴 ↔ (𝐹 Fn 𝐴 ∧ ran 𝐹 ⊆ V))
3 df-f 4956 . 2 (𝐹:𝐴⟶V ↔ (𝐹 Fn 𝐴 ∧ ran 𝐹 ⊆ V))
42, 3bitr4i 185 1 (𝐹 Fn 𝐴𝐹:𝐴⟶V)
Colors of variables: wff set class
Syntax hints:  wa 102  wb 103  Vcvv 2610  wss 2982  ran crn 4392   Fn wfn 4947  wf 4948
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-v 2612  df-in 2988  df-ss 2995  df-f 4956
This theorem is referenced by:  f1cnvcnv  5151  fcoconst  5386  fnressn  5401  1stcof  5841  2ndcof  5842  fnmpt2  5879  tposfn  5942  tfrlemibfn  5997  tfr1onlembfn  6013
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