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Definition df-plusf 15437
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 15452), while  +g only has closure (mndcl 15441). (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 15433 . 2  class  +f
2 vg . . 3  setvar  g
3 cvv 2993 . . 3  class  _V
4 vx . . . 4  setvar  x
5 vy . . . 4  setvar  y
62cv 1368 . . . . 5  class  g
7 cbs 14195 . . . . 5  class  Base
86, 7cfv 5439 . . . 4  class  ( Base `  g )
94cv 1368 . . . . 5  class  x
105cv 1368 . . . . 5  class  y
11 cplusg 14259 . . . . . 6  class  +g
126, 11cfv 5439 . . . . 5  class  ( +g  `  g )
139, 10, 12co 6112 . . . 4  class  ( x ( +g  `  g
) y )
144, 5, 8, 8, 13cmpt2 6114 . . 3  class  ( x  e.  ( Base `  g
) ,  y  e.  ( Base `  g
)  |->  ( x ( +g  `  g ) y ) )
152, 3, 14cmpt 4371 . 2  class  ( g  e.  _V  |->  ( x  e.  ( Base `  g
) ,  y  e.  ( Base `  g
)  |->  ( x ( +g  `  g ) y ) ) )
161, 15wceq 1369 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  15448
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