Theorem unt0 33050

Description: The null set is untangled. (Contributed by Scott Fenton, 10-Mar-2011.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)

Assertion

Ref	Expression
unt0	⊢ ∀𝑥 ∈ ∅ ¬ 𝑥 ∈ 𝑥

Proof of Theorem unt0

Step	Hyp	Ref	Expression
1		ral0 4414	1 ⊢ ∀𝑥 ∈ ∅ ¬ 𝑥 ∈ 𝑥

Syntax hints:  ¬ wn 3  ∀wral 3106  ∅c0 4243

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 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770

This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-ral 3111  df-dif 3884  df-nul 4244

This theorem is referenced by: (None)