Theorem 0nelfun 6452

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

Step	Hyp	Ref	Expression
1		funrel 6451	. 2 ⊢ (Fun 𝑅 → Rel 𝑅)
2		0nelrel 5648	. 2 ⊢ (Rel 𝑅 → ∅ ∉ 𝑅)
3	1, 2	syl 17	1 ⊢ (Fun 𝑅 → ∅ ∉ 𝑅)

Syntax hints:   → wi 4   ∉ wnel 3049  ∅c0 4256  Rel wrel 5594  Fun wfun 6427

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709  ax-sep 5223  ax-nul 5230  ax-pr 5352

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-ne 2944  df-nel 3050  df-v 3434  df-dif 3890  df-un 3892  df-in 3894  df-ss 3904  df-nul 4257  df-if 4460  df-sn 4562  df-pr 4564  df-op 4568  df-opab 5137  df-xp 5595  df-rel 5596  df-fun 6435

This theorem is referenced by: (None)