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Theorem dffn3 4996
Description: A function maps to its range. (Contributed by NM, 1-Sep-1999.)
Assertion
Ref Expression
dffn3 (𝐹 Fn A𝐹:A⟶ran 𝐹)

Proof of Theorem dffn3
StepHypRef Expression
1 ssid 2958 . . 3 ran 𝐹 ⊆ ran 𝐹
21biantru 286 . 2 (𝐹 Fn A ↔ (𝐹 Fn A ran 𝐹 ⊆ ran 𝐹))
3 df-f 4849 . 2 (𝐹:A⟶ran 𝐹 ↔ (𝐹 Fn A ran 𝐹 ⊆ ran 𝐹))
42, 3bitr4i 176 1 (𝐹 Fn A𝐹:A⟶ran 𝐹)
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98  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-in 2918  df-ss 2925  df-f 4849
This theorem is referenced by:  fsn2  5280  fo2ndf  5790
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