Metamath Recent Proofs http://us2.metamath.org:8888/mpeuni/mmrecent.html Recent proofs for Metamath proof system en 8472 : 0vfval Value of the function for the zero vecto... http://us2.metamath.org:8888/mpeuni/0vfval.html 5-Feb-2010   ⊢ G = ( +v ‘U)    &
   ⊢ Z = (0v ‘U)    ⇒
   ⊢ Z = (Id ‘G)
    ]]> 8275 : grpidval The value of the identity element of a g... http://us2.metamath.org:8888/mpeuni/grpidval.html 5-Feb-2010   ⊢ X = ran G    &
   ⊢ U = (Id ‘G)    ⇒
   ⊢ (G ∈ Grp → U = ∪{u ∈ X∣∀x ∈ X (uGx) = x})
    ]]> 8274 : grpidvallem The value of the identity element of a g... http://us2.metamath.org:8888/mpeuni/grpidvallem.html 5-Feb-2010   ⊢ X = ran G    &
   ⊢ U = (Id ‘G)    &
   ⊢ G ∈ Grp    ⇒
   ⊢ U = ∪{u ∈ X∣∀x ∈ X (uGx) = x}
    ]]> 8273 : grpsn The group operation for the singleton gr... http://us2.metamath.org:8888/mpeuni/grpsn.html 5-Feb-2010   ⊢ A ∈ V    ⇒
   ⊢ {<.<.A, A>., A>.} ∈ Grp
    ]]> 8272 : fungid Id is a function. (Contributed by FL, 5... http://us2.metamath.org:8888/mpeuni/fungid.html 5-Feb-2010   ⊢ Fun Id
    ]]> 8271 : gid0 The identity of the empty set is the emp... http://us2.metamath.org:8888/mpeuni/gid0.html 5-Feb-2010   ⊢ (Id ‘∅) = ∅
    ]]> 8270 : grprlidrid In a group a left and right identity ele... http://us2.metamath.org:8888/mpeuni/grprlidrid.html 5-Feb-2010   ⊢ X = ran G    ⇒
   ⊢ (G ∈ Grp → ∪{u ∈ X∣∀x ∈ X ((uGx) = x ⋀ (xGu) = x)} = ∪{u ∈ X∣∀x ∈ X (uGx) = x})
    ]]> 11609 : nrmsep2 In a normal space, any two disjoint clos... http://us2.metamath.org:8888/mpeuni/nrmsep2.html 1-Feb-2010   ⊢ ((J ∈ Nrm ⋀ (C ∈ (Clsd ‘J) ⋀ D ∈ (Clsd ‘J) ⋀ (C ∩ D) = ∅)) → ∃o ∈ J (C ⊆ o ⋀ (((cls ‘J) ‘o) ∩ D) = ∅))
    ]]> 11608 : nrmsep In a normal space, disjoint closed sets ... http://us2.metamath.org:8888/mpeuni/nrmsep.html 1-Feb-2010   ⊢ ((J ∈ Nrm ⋀ (C ∈ (Clsd ‘J) ⋀ D ∈ (Clsd ‘J) ⋀ (C ∩ D) = ∅)) → ∃o ∈ J ∃p ∈ J (C ⊆ o ⋀ D ⊆ p ⋀ (o ∩ p) = ∅))
    ]]> 11607 : nrmtop A normal space is a topological space. ... http://us2.metamath.org:8888/mpeuni/nrmtop.html 1-Feb-2010   ⊢ (J ∈ Nrm → J ∈ Top)]]>