MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-gic Structured version   Unicode version

Definition df-gic 15039
Description: Two groups are said to be isomorphic iff they are connected by at least one isomorphism. Isomophic groups share all global group properties, but to relate local properties requires knowledge of a specific isomorphism. (Contributed by Stefan O'Rear, 25-Jan-2015.)
Assertion
Ref Expression
df-gic  |-  ~=ph𝑔  =  ( `' GrpIso  " ( _V  \  1o ) )

Detailed syntax breakdown of Definition df-gic
StepHypRef Expression
1 cgic 15037 . 2  class  ~=ph𝑔
2 cgim 15036 . . . 4  class GrpIso
32ccnv 4869 . . 3  class  `' GrpIso
4 cvv 2948 . . . 4  class  _V
5 c1o 6709 . . . 4  class  1o
64, 5cdif 3309 . . 3  class  ( _V 
\  1o )
73, 6cima 4873 . 2  class  ( `' GrpIso  " ( _V  \  1o ) )
81, 7wceq 1652 1  wff  ~=ph𝑔  =  ( `' GrpIso  " ( _V  \  1o ) )
Colors of variables: wff set class
This definition is referenced by:  brgic  15048  gicer  15055
  Copyright terms: Public domain W3C validator