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Theorem 0nelfun 6520
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 6519 . 2 (Fun 𝑅 → Rel 𝑅)
2 0nelrel 5694 . 2 (Rel 𝑅 → ∅ ∉ 𝑅)
31, 2syl 17 1 (Fun 𝑅 → ∅ ∉ 𝑅)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wnel 3046  c0 4283  Rel wrel 5639  Fun wfun 6491
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-sep 5257  ax-nul 5264  ax-pr 5385
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ne 2941  df-nel 3047  df-v 3446  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-if 4488  df-sn 4588  df-pr 4590  df-op 4594  df-opab 5169  df-xp 5640  df-rel 5641  df-fun 6499
This theorem is referenced by: (None)
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