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Definition df-cnrm 17374
Description: Define completely normal spaces. A space is completely normal if all its subspaces are normal. (Contributed by Mario Carneiro, 26-Aug-2015.)
Assertion
Ref Expression
df-cnrm  |- CNrm  =  {
j  e.  Top  |  A. x  e.  ~P  U. j ( jt  x )  e.  Nrm }
Distinct variable group:    x, j

Detailed syntax breakdown of Definition df-cnrm
StepHypRef Expression
1 ccnrm 17367 . 2  class CNrm
2 vj . . . . . . 7  set  j
32cv 1651 . . . . . 6  class  j
4 vx . . . . . . 7  set  x
54cv 1651 . . . . . 6  class  x
6 crest 13640 . . . . . 6  classt
73, 5, 6co 6073 . . . . 5  class  ( jt  x )
8 cnrm 17366 . . . . 5  class  Nrm
97, 8wcel 1725 . . . 4  wff  ( jt  x )  e.  Nrm
103cuni 4007 . . . . 5  class  U. j
1110cpw 3791 . . . 4  class  ~P U. j
129, 4, 11wral 2697 . . 3  wff  A. x  e.  ~P  U. j ( jt  x )  e.  Nrm
13 ctop 16950 . . 3  class  Top
1412, 2, 13crab 2701 . 2  class  { j  e.  Top  |  A. x  e.  ~P  U. j
( jt  x )  e.  Nrm }
151, 14wceq 1652 1  wff CNrm  =  {
j  e.  Top  |  A. x  e.  ~P  U. j ( jt  x )  e.  Nrm }
Colors of variables: wff set class
This definition is referenced by:  iscnrm  17379
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