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Theorem dffun6 5286
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 2432 . 2  |-  F/_ x F
2 nfcv 2432 . 2  |-  F/_ y F
31, 2dffun6f 5285 1  |-  ( Fun 
F  <->  ( Rel  F  /\  A. x E* y  x F y ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358   A.wal 1530   E*wmo 2157   class class class wbr 4039   Rel wrel 4710   Fun wfun 5265
This theorem is referenced by:  funmo  5287  dffun7  5296  funcnvsn  5313  funcnv2  5325  svrelfun  5329  fnres  5376  nfunsn  5574  dff3  5689  brdom3  8169  nqerf  8570  shftfn  11584  perfdvf  19269  taylf  19756
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-opab 4094  df-id 4325  df-cnv 4713  df-co 4714  df-fun 5273
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