Users' Mathboxes Mathbox for Scott Fenton < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  unt0 Structured version   Visualization version   GIF version

Theorem unt0 31816
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 ∈ ∅ ¬ 𝑥𝑥

Proof of Theorem unt0
StepHypRef Expression
1 ral0 4184 1 𝑥 ∈ ∅ ¬ 𝑥𝑥
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wral 3014  c0 4023
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-9 2112  ax-10 2132  ax-11 2147  ax-12 2160  ax-13 2355  ax-ext 2704
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1599  df-ex 1818  df-nf 1823  df-sb 2011  df-clab 2711  df-cleq 2717  df-clel 2720  df-nfc 2855  df-ral 3019  df-v 3306  df-dif 3683  df-nul 4024
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator