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Theorem 0nelfun 6119
Description: A function does not contain the empty set. (Contributed by BJ, 26-Nov-2021.)
Assertion
Ref Expression
0nelfun (Fun 𝑅 → ∅ ∉ 𝑅)

Proof of Theorem 0nelfun
StepHypRef Expression
1 funrel 6118 . 2 (Fun 𝑅 → Rel 𝑅)
2 0nelrel 5367 . 2 (Rel 𝑅 → ∅ ∉ 𝑅)
31, 2syl 17 1 (Fun 𝑅 → ∅ ∉ 𝑅)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wnel 3074  c0 4115  Rel wrel 5317  Fun wfun 6095
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2377  ax-ext 2777  ax-sep 4975  ax-nul 4983  ax-pr 5097
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-3an 1110  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2786  df-cleq 2792  df-clel 2795  df-nfc 2930  df-ne 2972  df-nel 3075  df-v 3387  df-dif 3772  df-un 3774  df-in 3776  df-ss 3783  df-nul 4116  df-if 4278  df-sn 4369  df-pr 4371  df-op 4375  df-opab 4906  df-xp 5318  df-rel 5319  df-fun 6103
This theorem is referenced by: (None)
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