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Theorem 0nelfun 6349
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 6348 . 2 (Fun 𝑅 → Rel 𝑅)
2 0nelrel 5589 . 2 (Rel 𝑅 → ∅ ∉ 𝑅)
31, 2syl 17 1 (Fun 𝑅 → ∅ ∉ 𝑅)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wnel 3110  c0 4269  Rel wrel 5536  Fun wfun 6325
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2792  ax-sep 5179  ax-nul 5186  ax-pr 5306
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2799  df-cleq 2813  df-clel 2891  df-nfc 2959  df-ne 3007  df-nel 3111  df-v 3475  df-dif 3916  df-un 3918  df-in 3920  df-ss 3930  df-nul 4270  df-if 4444  df-sn 4544  df-pr 4546  df-op 4550  df-opab 5105  df-xp 5537  df-rel 5538  df-fun 6333
This theorem is referenced by: (None)
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