Theorem 0nelfun 6559

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 6558	. 2 ⊢ (Fun 𝑅 → Rel 𝑅)
2		0nelrel 5730	. 2 ⊢ (Rel 𝑅 → ∅ ∉ 𝑅)
3	1, 2	syl 17	1 ⊢ (Fun 𝑅 → ∅ ∉ 𝑅)

Syntax hints:   → wi 4   ∉ wnel 3040  ∅c0 4317  Rel wrel 5674  Fun wfun 6530

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697  ax-sep 5292  ax-nul 5299  ax-pr 5420

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-ne 2935  df-nel 3041  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-opab 5204  df-xp 5675  df-rel 5676  df-fun 6538

This theorem is referenced by: (None)