Database
REAL AND COMPLEX NUMBERS
Integer sets
Decimal arithmetic
dfdec10
Metamath Proof Explorer
Description: Version of the definition of the "decimal constructor" using ; 1 0
instead of the symbol 10. Of course, this statement cannot be used as
definition, because it uses the "decimal constructor". (Contributed by AV , 1-Aug-2021)
Ref
Expression
Assertion
dfdec10
Could not format assertion : No typesetting found for |- ; A B = ( ( ; 1 0 x. A ) + B ) with typecode |-
Proof
Step
Hyp
Ref
Expression
1
df-dec
Could not format ; A B = ( ( ( 9 + 1 ) x. A ) + B ) : No typesetting found for |- ; A B = ( ( ( 9 + 1 ) x. A ) + B ) with typecode |-
2
9p1e10
⊢ 9 + 1 = 10
3
2
oveq1i
⊢ 9 + 1 ⁢ A = 10 ⁢ A
4
3
oveq1i
⊢ 9 + 1 ⁢ A + B = 10 ⁢ A + B
5
1 4
eqtri
Could not format ; A B = ( ( ; 1 0 x. A ) + B ) : No typesetting found for |- ; A B = ( ( ; 1 0 x. A ) + B ) with typecode |-