New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  dffn2 Unicode version

Theorem dffn2 5224
 Description: Any function is a mapping into . (The proof was shortened by Andrew Salmon, 17-Sep-2011.) (Contributed by set.mm contributors, 31-Oct-1995.) (Revised by set.mm contributors, 18-Sep-2011.)
Assertion
Ref Expression
dffn2

Proof of Theorem dffn2
StepHypRef Expression
1 ssv 3291 . . 3
21biantru 491 . 2
3 df-f 4791 . 2
42, 3bitr4i 243 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358  cvv 2859   wss 3257   crn 4773   wfn 4776  wf 4777 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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:  fnressn  5438  fnmpt2  5732  xpassen  6057
 Copyright terms: Public domain W3C validator