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Theorem dffn3 5081
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 2992 . . 3 ran 𝐹 ⊆ ran 𝐹
21biantru 290 . 2 (𝐹 Fn 𝐴 ↔ (𝐹 Fn 𝐴 ∧ ran 𝐹 ⊆ ran 𝐹))
3 df-f 4934 . 2 (𝐹:𝐴⟶ran 𝐹 ↔ (𝐹 Fn 𝐴 ∧ ran 𝐹 ⊆ ran 𝐹))
42, 3bitr4i 180 1 (𝐹 Fn 𝐴𝐹:𝐴⟶ran 𝐹)
Colors of variables: wff set class
Syntax hints:  wa 101  wb 102  wss 2945  ran crn 4374   Fn wfn 4925  wf 4926
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-in 2952  df-ss 2959  df-f 4934
This theorem is referenced by:  fsn2  5365  fo2ndf  5876
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