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Theorem dffn3 5229
 Description: A function maps to its range. (Contributed by set.mm contributors, 1-Sep-1999.)
Assertion
Ref Expression
dffn3 (F Fn AF:A–→ran F)

Proof of Theorem dffn3
StepHypRef Expression
1 ssid 3290 . . 3 ran F ran F
21biantru 491 . 2 (F Fn A ↔ (F Fn A ran F ran F))
3 df-f 4791 . 2 (F:A–→ran F ↔ (F Fn A ran F ran F))
42, 3bitr4i 243 1 (F Fn AF:A–→ran F)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∧ wa 358   ⊆ 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  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-f 4791 This theorem is referenced by:  fsn2  5434
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