Theorem frn 5228

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 4791	. 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 3257  ran crn 4773   Fn wfn 4776  –→wf 4777

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 4791

This theorem is referenced by:  fssxp  5232  fcoi2  5241  fcnvres  5243  fimacnvdisj  5244  f00  5249  foconst  5280  fun11iun  5305  fimacnv  5411  ffvelrn  5415  fnfvrnss  5429  map0b  6024  mapsn  6026  enprmaplem3  6078  dflec3  6221