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Theorem funforn 6337
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 6130 . 2 (Fun 𝐴𝐴 Fn dom 𝐴)
2 dffn4 6336 . 2 (𝐴 Fn dom 𝐴𝐴:dom 𝐴onto→ran 𝐴)
31, 2bitri 267 1 (Fun 𝐴𝐴:dom 𝐴onto→ran 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wb 198  dom cdm 5311  ran crn 5312  Fun wfun 6094   Fn wfn 6095  ontowfo 6098
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-ext 2776
This theorem depends on definitions:  df-bi 199  df-an 386  df-ex 1876  df-cleq 2791  df-fn 6103  df-fo 6106
This theorem is referenced by:  fimacnvinrn  6573  imacosupp  7572  ordtypelem8  8671  wdomima2g  8732  imadomg  9643  gruima  9911  oppglsm  18367  1stcrestlem  21581  dfac14  21747  qtoptop2  21828
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