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Theorem dffn2 4990
 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 2959 . . 3 ran 𝐹 ⊆ V
21biantru 286 . 2 (𝐹 Fn A ↔ (𝐹 Fn A ran 𝐹 ⊆ V))
3 df-f 4849 . 2 (𝐹:A⟶V ↔ (𝐹 Fn A ran 𝐹 ⊆ V))
42, 3bitr4i 176 1 (𝐹 Fn A𝐹:A⟶V)
 Colors of variables: wff set class Syntax hints:   ∧ wa 97   ↔ wb 98  Vcvv 2551   ⊆ wss 2911  ran crn 4289   Fn wfn 4840  ⟶wf 4841 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-v 2553  df-in 2918  df-ss 2925  df-f 4849 This theorem is referenced by:  f1cnvcnv  5043  fcoconst  5277  fnressn  5292  1stcof  5732  2ndcof  5733  fnmpt2  5770  tposfn  5829  tfrlemibfn  5883
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