Theorem unt0 35743

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 4463	1 ⊢ ∀𝑥 ∈ ∅ ¬ 𝑥 ∈ 𝑥

Syntax hints:  ¬ wn 3  ∀wral 3047  ∅c0 4283

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-ral 3048  df-dif 3905  df-nul 4284

This theorem is referenced by: (None)