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Theorem dffun6 6052
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 ∧ ∀𝑥∃*𝑦 𝑥𝐹𝑦))
Distinct variable group:   𝑥,𝑦,𝐹

Proof of Theorem dffun6
StepHypRef Expression
1 nfcv 2890 . 2 𝑥𝐹
2 nfcv 2890 . 2 𝑦𝐹
31, 2dffun6f 6051 1 (Fun 𝐹 ↔ (Rel 𝐹 ∧ ∀𝑥∃*𝑦 𝑥𝐹𝑦))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 383  wal 1618  ∃*wmo 2596   class class class wbr 4792  Rel wrel 5259  Fun wfun 6031
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1859  ax-4 1874  ax-5 1976  ax-6 2042  ax-7 2078  ax-9 2136  ax-10 2156  ax-11 2171  ax-12 2184  ax-13 2379  ax-ext 2728  ax-sep 4921  ax-nul 4929  ax-pr 5043
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1623  df-ex 1842  df-nf 1847  df-sb 2035  df-eu 2599  df-mo 2600  df-clab 2735  df-cleq 2741  df-clel 2744  df-nfc 2879  df-ral 3043  df-rab 3047  df-v 3330  df-dif 3706  df-un 3708  df-in 3710  df-ss 3717  df-nul 4047  df-if 4219  df-sn 4310  df-pr 4312  df-op 4316  df-br 4793  df-opab 4853  df-id 5162  df-cnv 5262  df-co 5263  df-fun 6039
This theorem is referenced by:  funmo  6053  dffun7  6064  fununfun  6083  funcnvsn  6085  funcnv2  6106  svrelfun  6110  fnres  6156  nfunsn  6374  dff3  6523  brdom3  9513  nqerf  9915  shftfn  13983  cnextfun  22040  perfdvf  23837  taylf  24285
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