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Theorem 0nelfun 6577
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 6576 . 2 (Fun 𝑅 → Rel 𝑅)
2 0nelrel 5743 . 2 (Rel 𝑅 → ∅ ∉ 𝑅)
31, 2syl 17 1 (Fun 𝑅 → ∅ ∉ 𝑅)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wnel 3036  c0 4325  Rel wrel 5687  Fun wfun 6548
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2697  ax-sep 5304  ax-nul 5311  ax-pr 5433
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2704  df-cleq 2718  df-clel 2803  df-ne 2931  df-nel 3037  df-v 3464  df-dif 3950  df-un 3952  df-ss 3964  df-nul 4326  df-if 4534  df-sn 4634  df-pr 4636  df-op 4640  df-opab 5216  df-xp 5688  df-rel 5689  df-fun 6556
This theorem is referenced by: (None)
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