Theorem 0nelfun 6596

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 6595	. 2 ⊢ (Fun 𝑅 → Rel 𝑅)
2		0nelrel 5761	. 2 ⊢ (Rel 𝑅 → ∅ ∉ 𝑅)
3	1, 2	syl 17	1 ⊢ (Fun 𝑅 → ∅ ∉ 𝑅)

Syntax hints:   → wi 4   ∉ wnel 3052  ∅c0 4352  Rel wrel 5705  Fun wfun 6567

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711  ax-sep 5317  ax-nul 5324  ax-pr 5447

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-ne 2947  df-nel 3053  df-v 3490  df-dif 3979  df-un 3981  df-ss 3993  df-nul 4353  df-if 4549  df-sn 4649  df-pr 4651  df-op 4655  df-opab 5229  df-xp 5706  df-rel 5707  df-fun 6575

This theorem is referenced by: (None)