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Definition df-plusf 16193
Description: Define group addition function. Usually we will use 
+g directly instead of  +f, and they have the same behavior in most cases. The main advantage of  +f for any magma is that it is a guaranteed function (mgmplusf 16203), while  +g only has closure (mgmcl 16197). (Contributed by Mario Carneiro, 14-Aug-2015.)
Assertion
Ref Expression
df-plusf  |-  +f 
=  ( g  e. 
_V  |->  ( x  e.  ( Base `  g
) ,  y  e.  ( Base `  g
)  |->  ( x ( +g  `  g ) y ) ) )
Distinct variable group:    x, g, y

Detailed syntax breakdown of Definition df-plusf
StepHypRef Expression
1 cplusf 16191 . 2  class  +f
2 vg . . 3  setvar  g
3 cvv 3058 . . 3  class  _V
4 vx . . . 4  setvar  x
5 vy . . . 4  setvar  y
62cv 1404 . . . . 5  class  g
7 cbs 14839 . . . . 5  class  Base
86, 7cfv 5568 . . . 4  class  ( Base `  g )
94cv 1404 . . . . 5  class  x
105cv 1404 . . . . 5  class  y
11 cplusg 14907 . . . . . 6  class  +g
126, 11cfv 5568 . . . . 5  class  ( +g  `  g )
139, 10, 12co 6277 . . . 4  class  ( x ( +g  `  g
) y )
144, 5, 8, 8, 13cmpt2 6279 . . 3  class  ( x  e.  ( Base `  g
) ,  y  e.  ( Base `  g
)  |->  ( x ( +g  `  g ) y ) )
152, 3, 14cmpt 4452 . 2  class  ( g  e.  _V  |->  ( x  e.  ( Base `  g
) ,  y  e.  ( Base `  g
)  |->  ( x ( +g  `  g ) y ) ) )
161, 15wceq 1405 1  wff  +f 
=  ( g  e. 
_V  |->  ( x  e.  ( Base `  g
) ,  y  e.  ( Base `  g
)  |->  ( x ( +g  `  g ) y ) ) )
Colors of variables: wff setvar class
This definition is referenced by:  plusffval  16199
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