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Theorem dffun6 5805
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 2750 . 2 𝑥𝐹
2 nfcv 2750 . 2 𝑦𝐹
31, 2dffun6f 5804 1 (Fun 𝐹 ↔ (Rel 𝐹 ∧ ∀𝑥∃*𝑦 𝑥𝐹𝑦))
Colors of variables: wff setvar class
Syntax hints:  wb 194  wa 382  wal 1472  ∃*wmo 2458   class class class wbr 4577  Rel wrel 5033  Fun wfun 5784
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-9 1985  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589  ax-sep 4703  ax-nul 4712  ax-pr 4828
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-3an 1032  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-eu 2461  df-mo 2462  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-ral 2900  df-rab 2904  df-v 3174  df-dif 3542  df-un 3544  df-in 3546  df-ss 3553  df-nul 3874  df-if 4036  df-sn 4125  df-pr 4127  df-op 4131  df-br 4578  df-opab 4638  df-id 4943  df-cnv 5036  df-co 5037  df-fun 5792
This theorem is referenced by:  funmo  5806  dffun7  5816  fununfun  5834  funcnvsn  5836  funcnv2  5857  svrelfun  5861  fnres  5907  nfunsn  6120  dff3  6265  brdom3  9208  nqerf  9608  shftfn  13607  cnextfun  21620  perfdvf  23390  taylf  23836
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