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Theorem dffun6 4916
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 2178 . 2  |-  F/_ x F
2 nfcv 2178 . 2  |-  F/_ y F
31, 2dffun6f 4915 1  |-  ( Fun 
F  <->  ( Rel  F  /\  A. x E* y  x F y ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 97    <-> wb 98   A.wal 1241   E*wmo 1901   class class class wbr 3764   Rel wrel 4350   Fun wfun 4896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944
This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-opab 3819  df-id 4030  df-cnv 4353  df-co 4354  df-fun 4904
This theorem is referenced by:  funmo  4917  dffun7  4928  funcnvsn  4945  funcnv2  4959  svrelfun  4964  fnres  5015  nfunsn  5207  shftfn  9425
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