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Theorem 0nelfun 5148
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 5147 . 2  |-  ( Fun 
R  ->  Rel  R )
2 0nelrel 4592 . 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 2404   (/)c0 3367   Rel wrel 4551   Fun wfun 5124
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-14 1493  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4053  ax-pow 4105  ax-pr 4138
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-fal 1338  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ne 2310  df-nel 2405  df-v 2691  df-dif 3077  df-un 3079  df-in 3081  df-ss 3088  df-nul 3368  df-pw 3516  df-sn 3537  df-pr 3538  df-op 3540  df-opab 3997  df-xp 4552  df-rel 4553  df-fun 5132
This theorem is referenced by: (None)
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