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Theorem ffrn 6732
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 6718 . 2 (๐น:๐ดโŸถ๐ต โ†’ ๐น Fn ๐ด)
2 dffn3 6731 . 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 5678   Fn wfn 6539  โŸถwf 6540
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 3477  df-in 3956  df-ss 3966  df-f 6548
This theorem is referenced by:  fo2ndf  8107  mapsnd  8880  itg1val2  25201  volicoff  44711  f1cof1b  45785  f1ocof1ob  45789  fundcmpsurbijinjpreimafv  46075
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