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Theorem dffun6 6349
 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 2979 . 2 𝑥𝐹
2 nfcv 2979 . 2 𝑦𝐹
31, 2dffun6f 6348 1 (Fun 𝐹 ↔ (Rel 𝐹 ∧ ∀𝑥∃*𝑦 𝑥𝐹𝑦))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 209   ∧ wa 399  ∀wal 1536  ∃*wmo 2620   class class class wbr 5042  Rel wrel 5537  Fun wfun 6328 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2178  ax-ext 2794  ax-sep 5179  ax-nul 5186  ax-pr 5307 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2622  df-eu 2653  df-clab 2801  df-cleq 2815  df-clel 2894  df-nfc 2962  df-ral 3135  df-v 3471  df-dif 3911  df-un 3913  df-in 3915  df-ss 3925  df-nul 4266  df-if 4440  df-sn 4540  df-pr 4542  df-op 4546  df-br 5043  df-opab 5105  df-id 5437  df-cnv 5540  df-co 5541  df-fun 6336 This theorem is referenced by:  funmo  6350  dffun7  6361  fununfun  6381  funcnvsn  6383  funcnv2  6401  svrelfun  6405  fnres  6454  nfunsn  6689  dff3  6848  brdom3  9939  nqerf  10341  shftfn  14423  cnextfun  22667  perfdvf  24504  taylf  24954  funressnvmo  43577
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