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Theorem funforn 6590
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 6378 . 2 (Fun 𝐴𝐴 Fn dom 𝐴)
2 dffn4 6589 . 2 (𝐴 Fn dom 𝐴𝐴:dom 𝐴onto→ran 𝐴)
31, 2bitri 277 1 (Fun 𝐴𝐴:dom 𝐴onto→ran 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wb 208  dom cdm 5548  ran crn 5549  Fun wfun 6342   Fn wfn 6343  ontowfo 6346
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1905  ax-6 1964  ax-7 2009  ax-9 2118  ax-ext 2791
This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1775  df-cleq 2812  df-fn 6351  df-fo 6354
This theorem is referenced by:  fimacnvinrn  6833  imacosupp  7866  imacosuppOLD  7867  ordtypelem8  8981  wdomima2g  9042  imadomg  9948  gruima  10216  oppglsm  18759  1stcrestlem  22052  dfac14  22218  qtoptop2  22299
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