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Theorem funforn 6089
Description: A function maps its domain onto its range. (Contributed by NM, 23-Jul-2004.)
Assertion
Ref Expression
funforn (Fun 𝐴𝐴:dom 𝐴onto→ran 𝐴)

Proof of Theorem funforn
StepHypRef Expression
1 funfn 5887 . 2 (Fun 𝐴𝐴 Fn dom 𝐴)
2 dffn4 6088 . 2 (𝐴 Fn dom 𝐴𝐴:dom 𝐴onto→ran 𝐴)
31, 2bitri 264 1 (Fun 𝐴𝐴:dom 𝐴onto→ran 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wb 196  dom cdm 5084  ran crn 5085  Fun wfun 5851   Fn wfn 5852  ontowfo 5855
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1702  df-cleq 2614  df-fn 5860  df-fo 5863
This theorem is referenced by:  fimacnvinrn  6314  imacosupp  7295  ordtypelem8  8390  wdomima2g  8451  imadomg  9316  gruima  9584  oppglsm  17997  1stcrestlem  21195  dfac14  21361  qtoptop2  21442
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