Theorem ffrn 5522

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 5510	. 2 |- ( F : A --> B -> F Fn A )
2		dffn3 5521	. 2 |- ( F Fn A <-> F : A --> ran F )
3	1, 2	sylib 122	1 |- ( F : A --> B -> F : A --> ran F )

Syntax hints:   -> wi 4   ran crn 4752   Fn wfn 5349   -->wf 5350

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-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-in 3219  df-ss 3226  df-f 5358

This theorem is referenced by:  mapsnd  6925