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Definition df-dec 9176
Description: Define the "decimal constructor", which is used to build up "decimal integers" or "numeric terms" in base  1
0. For example,  (;;; 1 0 0 0  + ;;; 2 0 0 0 )  = ;;; 3 0 0 0 1kp2ke3k 12925. (Contributed by Mario Carneiro, 17-Apr-2015.) (Revised by AV, 1-Aug-2021.)
Assertion
Ref Expression
df-dec  |- ; A B  =  ( ( ( 9  +  1 )  x.  A
)  +  B )

Detailed syntax breakdown of Definition df-dec
StepHypRef Expression
1 cA . . 3  class  A
2 cB . . 3  class  B
31, 2cdc 9175 . 2  class ; A B
4 c9 8771 . . . . 5  class  9
5 c1 7614 . . . . 5  class  1
6 caddc 7616 . . . . 5  class  +
74, 5, 6co 5767 . . . 4  class  ( 9  +  1 )
8 cmul 7618 . . . 4  class  x.
97, 1, 8co 5767 . . 3  class  ( ( 9  +  1 )  x.  A )
109, 2, 6co 5767 . 2  class  ( ( ( 9  +  1 )  x.  A )  +  B )
113, 10wceq 1331 1  wff ; A B  =  ( ( ( 9  +  1 )  x.  A
)  +  B )
Colors of variables: wff set class
This definition is referenced by:  9p1e10  9177  dfdec10  9178  deceq1  9179  deceq2  9180  deccl  9189
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