Theorem 0nelfun 6511

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 6510	. 2 ⊢ (Fun 𝑅 → Rel 𝑅)
2		0nelrel 5686	. 2 ⊢ (Rel 𝑅 → ∅ ∉ 𝑅)
3	1, 2	syl 17	1 ⊢ (Fun 𝑅 → ∅ ∉ 𝑅)

Syntax hints:   → wi 4   ∉ wnel 3037  ∅c0 4286  Rel wrel 5630  Fun wfun 6487

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-sep 5242  ax-nul 5252  ax-pr 5378

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-ne 2934  df-nel 3038  df-v 3443  df-dif 3905  df-un 3907  df-ss 3919  df-nul 4287  df-if 4481  df-sn 4582  df-pr 4584  df-op 4588  df-opab 5162  df-xp 5631  df-rel 5632  df-fun 6495

This theorem is referenced by: (None)