Theorem frn 5229

Description: The range of a mapping. (Contributed by set.mm contributors, 3-Aug-1994.)

Assertion

Ref	Expression
frn	⊢ (F:A–→B → ran F ⊆ B)

Proof of Theorem frn

Step	Hyp	Ref	Expression
1		df-f 4792	. 2 ⊢ (F:A–→B ↔ (F Fn A ∧ ran F ⊆ B))
2	1	simprbi 450	1 ⊢ (F:A–→B → ran F ⊆ B)

Syntax hints:   → wi 4   ⊆ wss 3258  ran crn 4774   Fn wfn 4777  –→wf 4778

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 177  df-an 360  df-f 4792

This theorem is referenced by:  fssxp  5233  fcoi2  5242  fcnvres  5244  fimacnvdisj  5245  f00  5250  foconst  5281  fun11iun  5306  fimacnv  5412  ffvelrn  5416  fnfvrnss  5430  map0b  6025  mapsn  6027  enprmaplem3  6079  dflec3  6222