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Theorem dffun6 5609
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 2629 . 2  |-  F/_ x F
2 nfcv 2629 . 2  |-  F/_ y F
31, 2dffun6f 5608 1  |-  ( Fun 
F  <->  ( Rel  F  /\  A. x E* y  x F y ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369   A.wal 1377   E*wmo 2276   class class class wbr 4453   Rel wrel 5010   Fun wfun 5588
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4574  ax-nul 4582  ax-pr 4692
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2822  df-rab 2826  df-v 3120  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-sn 4034  df-pr 4036  df-op 4040  df-br 4454  df-opab 4512  df-id 4801  df-cnv 5013  df-co 5014  df-fun 5596
This theorem is referenced by:  funmo  5610  dffun7  5620  fununfun  5638  funcnvsn  5639  funcnv2  5653  svrelfun  5657  fnres  5703  nfunsn  5903  dff3  6045  brdom3  8918  nqerf  9320  shftfn  12886  cnextfun  20432  perfdvf  22175  taylf  22623
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