ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  0nelfun Unicode version

Theorem 0nelfun 5249
Description: A function does not contain the empty set. (Contributed by BJ, 26-Nov-2021.)
Assertion
Ref Expression
0nelfun  |-  ( Fun 
R  ->  (/)  e/  R
)

Proof of Theorem 0nelfun
StepHypRef Expression
1 funrel 5248 . 2  |-  ( Fun 
R  ->  Rel  R )
2 0nelrel 4687 . 2  |-  ( Rel 
R  ->  (/)  e/  R
)
31, 2syl 14 1  |-  ( Fun 
R  ->  (/)  e/  R
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    e/ wnel 2455   (/)c0 3437   Rel wrel 4646   Fun wfun 5225
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-14 2163  ax-ext 2171  ax-sep 4136  ax-pow 4189  ax-pr 4224
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-fal 1370  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ne 2361  df-nel 2456  df-v 2754  df-dif 3146  df-un 3148  df-in 3150  df-ss 3157  df-nul 3438  df-pw 3592  df-sn 3613  df-pr 3614  df-op 3616  df-opab 4080  df-xp 4647  df-rel 4648  df-fun 5233
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator