ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  dffun6 GIF version

Theorem dffun6 5016
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 2228 . 2 𝑥𝐹
2 nfcv 2228 . 2 𝑦𝐹
31, 2dffun6f 5015 1 (Fun 𝐹 ↔ (Rel 𝐹 ∧ ∀𝑥∃*𝑦 𝑥𝐹𝑦))
Colors of variables: wff set class
Syntax hints:  wa 102  wb 103  wal 1287  ∃*wmo 1949   class class class wbr 3837  Rel wrel 4433  Fun wfun 4996
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-14 1450  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-sep 3949  ax-pow 4001  ax-pr 4027
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-v 2621  df-un 3001  df-in 3003  df-ss 3010  df-pw 3427  df-sn 3447  df-pr 3448  df-op 3450  df-br 3838  df-opab 3892  df-id 4111  df-cnv 4436  df-co 4437  df-fun 5004
This theorem is referenced by:  funmo  5017  dffun7  5028  funcnvsn  5045  funcnv2  5060  svrelfun  5065  fnres  5116  nfunsn  5322  shftfn  10223
  Copyright terms: Public domain W3C validator