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Theorem dffun6 6046
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 2913 . 2 𝑥𝐹
2 nfcv 2913 . 2 𝑦𝐹
31, 2dffun6f 6045 1 (Fun 𝐹 ↔ (Rel 𝐹 ∧ ∀𝑥∃*𝑦 𝑥𝐹𝑦))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 382  wal 1629  ∃*wmo 2619   class class class wbr 4786  Rel wrel 5254  Fun wfun 6025
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751  ax-sep 4915  ax-nul 4923  ax-pr 5034
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-3an 1073  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-eu 2622  df-mo 2623  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-ral 3066  df-rab 3070  df-v 3353  df-dif 3726  df-un 3728  df-in 3730  df-ss 3737  df-nul 4064  df-if 4226  df-sn 4317  df-pr 4319  df-op 4323  df-br 4787  df-opab 4847  df-id 5157  df-cnv 5257  df-co 5258  df-fun 6033
This theorem is referenced by:  funmo  6047  dffun7  6058  fununfun  6077  funcnvsn  6079  funcnv2  6097  svrelfun  6101  fnres  6147  nfunsn  6366  dff3  6515  brdom3  9552  nqerf  9954  shftfn  14021  cnextfun  22088  perfdvf  23887  taylf  24335
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