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Theorem frnd 39944
Description: The range of a mapping. (Contributed by Glauco Siliprandi, 26-Jun-2021.)
Hypothesis
Ref Expression
frnd.1 (𝜑𝐹:𝐴𝐵)
Assertion
Ref Expression
frnd (𝜑 → ran 𝐹𝐵)

Proof of Theorem frnd
StepHypRef Expression
1 frnd.1 . 2 (𝜑𝐹:𝐴𝐵)
2 frn 6193 . 2 (𝐹:𝐴𝐵 → ran 𝐹𝐵)
31, 2syl 17 1 (𝜑 → ran 𝐹𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3723  ran crn 5250  wf 6027
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-an 383  df-f 6035
This theorem is referenced by:  climinf2lem  40456  limsupvaluz2  40488  supcnvlimsup  40490  limsupgtlem  40527  preimaioomnf  41449  smfco  41529
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