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Theorem funforn 6283
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 6079 . 2 (Fun 𝐴𝐴 Fn dom 𝐴)
2 dffn4 6282 . 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 5266  ran crn 5267  Fun wfun 6043   Fn wfn 6044  ontowfo 6047
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-ext 2740
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1854  df-cleq 2753  df-fn 6052  df-fo 6055
This theorem is referenced by:  fimacnvinrn  6511  imacosupp  7504  ordtypelem8  8595  wdomima2g  8656  imadomg  9548  gruima  9816  oppglsm  18257  1stcrestlem  21457  dfac14  21623  qtoptop2  21704
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