Theorem unt0 33648

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 4449	1 ⊢ ∀𝑥 ∈ ∅ ¬ 𝑥 ∈ 𝑥

Syntax hints:  ¬ wn 3  ∀wral 3066  ∅c0 4262

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2015  ax-9 2120  ax-ext 2711

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1545  df-fal 1555  df-ex 1787  df-sb 2072  df-clab 2718  df-cleq 2732  df-ral 3071  df-dif 3895  df-nul 4263

This theorem is referenced by: (None)