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Definition df-plusf 14368
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 is that it is a guaranteed function (mndplusf 14383), while  +g only has closure (mndcl 14372). (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 14364 . 2  class  + f
2 vg . . 3  set  g
3 cvv 2788 . . 3  class  _V
4 vx . . . 4  set  x
5 vy . . . 4  set  y
62cv 1622 . . . . 5  class  g
7 cbs 13148 . . . . 5  class  Base
86, 7cfv 5255 . . . 4  class  ( Base `  g )
94cv 1622 . . . . 5  class  x
105cv 1622 . . . . 5  class  y
11 cplusg 13208 . . . . . 6  class  +g
126, 11cfv 5255 . . . . 5  class  ( +g  `  g )
139, 10, 12co 5858 . . . 4  class  ( x ( +g  `  g
) y )
144, 5, 8, 8, 13cmpt2 5860 . . 3  class  ( x  e.  ( Base `  g
) ,  y  e.  ( Base `  g
)  |->  ( x ( +g  `  g ) y ) )
152, 3, 14cmpt 4077 . 2  class  ( g  e.  _V  |->  ( x  e.  ( Base `  g
) ,  y  e.  ( Base `  g
)  |->  ( x ( +g  `  g ) y ) ) )
161, 15wceq 1623 1  wff  + f  =  ( g  e. 
_V  |->  ( x  e.  ( Base `  g
) ,  y  e.  ( Base `  g
)  |->  ( x ( +g  `  g ) y ) ) )
Colors of variables: wff set class
This definition is referenced by:  plusffval  14379
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