Theorem unt0 35711

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 4513	1 ⊢ ∀𝑥 ∈ ∅ ¬ 𝑥 ∈ 𝑥

Syntax hints:  ¬ wn 3  ∀wral 3061  ∅c0 4333

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-9 2118  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-ral 3062  df-dif 3954  df-nul 4334

This theorem is referenced by: (None)