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Theorem f1rn 5217
Description: The range of a one-to-one mapping. (Contributed by BJ, 6-Jul-2022.)
Assertion
Ref Expression
f1rn (𝐹:𝐴1-1𝐵 → ran 𝐹𝐵)

Proof of Theorem f1rn
StepHypRef Expression
1 f1f 5216 . 2 (𝐹:𝐴1-1𝐵𝐹:𝐴𝐵)
2 frn 5169 . 2 (𝐹:𝐴𝐵 → ran 𝐹𝐵)
31, 2syl 14 1 (𝐹:𝐴1-1𝐵 → ran 𝐹𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4  wss 2999  ran crn 4439  wf 5011  1-1wf1 5012
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105
This theorem depends on definitions:  df-bi 115  df-f 5019  df-f1 5020
This theorem is referenced by:  fun11iun  5274  f1dmex  5887  f1finf1o  6654  djuun  6758  caserel  6776  djudom  6785  exmidfodomrlemim  6825
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