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Theorem ffrn 6683
Description: A function maps to its range. (Contributed by Glauco Siliprandi, 3-Mar-2021.)
Assertion
Ref Expression
ffrn (๐น:๐ดโŸถ๐ต โ†’ ๐น:๐ดโŸถran ๐น)

Proof of Theorem ffrn
StepHypRef Expression
1 ffn 6669 . 2 (๐น:๐ดโŸถ๐ต โ†’ ๐น Fn ๐ด)
2 dffn3 6682 . 2 (๐น Fn ๐ด โ†” ๐น:๐ดโŸถran ๐น)
31, 2sylib 217 1 (๐น:๐ดโŸถ๐ต โ†’ ๐น:๐ดโŸถran ๐น)
Colors of variables: wff setvar class
Syntax hints:   โ†’ wi 4  ran crn 5635   Fn wfn 6492  โŸถwf 6493
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3446  df-in 3918  df-ss 3928  df-f 6501
This theorem is referenced by:  fo2ndf  8054  mapsnd  8827  itg1val2  25064  volicoff  44322  f1cof1b  45395  f1ocof1ob  45399  fundcmpsurbijinjpreimafv  45685
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