Theorem ffrn 5545

Description: A function maps to its range. (Contributed by Glauco Siliprandi, 3-Mar-2021.)

Assertion

Ref	Expression
ffrn	|- ( F : A --> B -> F : A --> ran F )

Proof of Theorem ffrn

Step	Hyp	Ref	Expression
1		ffn 5533	. 2 |- ( F : A --> B -> F Fn A )
2		dffn3 5544	. 2 |- ( F Fn A <-> F : A --> ran F )
3	1, 2	sylib 122	1 |- ( F : A --> B -> F : A --> ran F )

This proof depends on syntax axioms:   -> wi 4   ran crn 4775   Fn wfn 5372   -->wf 5373

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-in 3226  df-ss 3233  df-f 5381

This theorem is used by:  mapsnd  6970