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Theorem 0nelfun 5246
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 5245 . 2  |-  ( Fun 
R  ->  Rel  R )
2 0nelrel 4684 . 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 2452   (/)c0 3434   Rel wrel 4643   Fun wfun 5222
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 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-14 2161  ax-ext 2169  ax-sep 4133  ax-pow 4186  ax-pr 4221
This theorem depends on definitions:  df-bi 117  df-3an 981  df-tru 1366  df-fal 1369  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-ne 2358  df-nel 2453  df-v 2751  df-dif 3143  df-un 3145  df-in 3147  df-ss 3154  df-nul 3435  df-pw 3589  df-sn 3610  df-pr 3611  df-op 3613  df-opab 4077  df-xp 4644  df-rel 4645  df-fun 5230
This theorem is referenced by: (None)
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