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Theorem dffun6 5016
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 2228 . 2  |-  F/_ x F
2 nfcv 2228 . 2  |-  F/_ y F
31, 2dffun6f 5015 1  |-  ( Fun 
F  <->  ( Rel  F  /\  A. x E* y  x F y ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 102    <-> wb 103   A.wal 1287   E*wmo 1949   class class class wbr 3837   Rel wrel 4433   Fun wfun 4996
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-14 1450  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-sep 3949  ax-pow 4001  ax-pr 4027
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-v 2621  df-un 3001  df-in 3003  df-ss 3010  df-pw 3427  df-sn 3447  df-pr 3448  df-op 3450  df-br 3838  df-opab 3892  df-id 4111  df-cnv 4436  df-co 4437  df-fun 5004
This theorem is referenced by:  funmo  5017  dffun7  5028  funcnvsn  5045  funcnv2  5060  svrelfun  5065  fnres  5116  nfunsn  5322  shftfn  10223
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