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Theorem funforn 5445
Description: A function maps its domain onto its range. (Contributed by NM, 23-Jul-2004.)
Assertion
Ref Expression
funforn (Fun 𝐴 ↔ 𝐴:dom 𝐴–ontoβ†’ran 𝐴)

Proof of Theorem funforn
StepHypRef Expression
1 funfn 5246 . 2 (Fun 𝐴 ↔ 𝐴 Fn dom 𝐴)
2 dffn4 5444 . 2 (𝐴 Fn dom 𝐴 ↔ 𝐴:dom 𝐴–ontoβ†’ran 𝐴)
31, 2bitri 184 1 (Fun 𝐴 ↔ 𝐴:dom 𝐴–ontoβ†’ran 𝐴)
Colors of variables: wff set class
Syntax hints:   ↔ wb 105  dom cdm 4626  ran crn 4627  Fun wfun 5210   Fn wfn 5211  β€“ontoβ†’wfo 5214
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1449  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-fn 5219  df-fo 5222
This theorem is referenced by:  dvrecap  14147
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