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Theorem funforn 6827
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 6596 . 2 (Fun 𝐴𝐴 Fn dom 𝐴)
2 dffn4 6826 . 2 (𝐴 Fn dom 𝐴𝐴:dom 𝐴onto→ran 𝐴)
31, 2bitri 275 1 (Fun 𝐴𝐴:dom 𝐴onto→ran 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wb 206  dom cdm 5685  ran crn 5686  Fun wfun 6555   Fn wfn 6556  ontowfo 6559
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-cleq 2729  df-fn 6564  df-fo 6567
This theorem is referenced by:  fimacnvinrn  7091  imacosupp  8234  ordtypelem8  9565  wdomima2g  9626  imadomg  10574  gruima  10842  oppglsm  19660  1stcrestlem  23460  dfac14  23626  qtoptop2  23707  fsupprnfi  32701  imadomfi  42003  rn1st  45280
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