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Theorem f1rn 5324
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 5323 . 2 (𝐹:𝐴1-1𝐵𝐹:𝐴𝐵)
2 frn 5276 . 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 3066  ran crn 4535  wf 5114  1-1wf1 5115
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106
This theorem depends on definitions:  df-bi 116  df-f 5122  df-f1 5123
This theorem is referenced by:  fun11iun  5381  f1dmex  6007  f1finf1o  6828  caserel  6965  djudom  6971  exmidfodomrlemim  7050
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