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Theorem dffun6 5469
Description: Alternate definition of a function using "at most one" notation. (Contributed by NM, 9-Mar-1995.)
Assertion
Ref Expression
dffun6  |-  ( Fun 
F  <->  ( Rel  F  /\  A. x E* y  x F y ) )
Distinct variable group:    x, y, F

Proof of Theorem dffun6
StepHypRef Expression
1 nfcv 2572 . 2  |-  F/_ x F
2 nfcv 2572 . 2  |-  F/_ y F
31, 2dffun6f 5468 1  |-  ( Fun 
F  <->  ( Rel  F  /\  A. x E* y  x F y ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359   A.wal 1549   E*wmo 2282   class class class wbr 4212   Rel wrel 4883   Fun wfun 5448
This theorem is referenced by:  funmo  5470  dffun7  5479  funcnvsn  5496  funcnv2  5510  svrelfun  5514  fnres  5561  nfunsn  5761  dff3  5882  brdom3  8406  nqerf  8807  shftfn  11888  cnextfun  18095  perfdvf  19790  taylf  20277
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-id 4498  df-cnv 4886  df-co 4887  df-fun 5456
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