Theorem dpval

Description: Define the value of the decimal point operator. See df-dp . (Contributed by David A. Wheeler, 15-May-2015)

	Ref	Expression
Assertion	dpval	Could not format assertion : No typesetting found for |- ( ( A e. NN0 /\ B e. RR ) -> ( A . B ) = _ A B ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		df-dp2	Could not format _ x y = ( x + ( y / ; 1 0 ) ) : No typesetting found for |- _ x y = ( x + ( y / ; 1 0 ) ) with typecode |-
2		oveq1	$$⊢x=A\to x+\left(\frac{y}{10}\right)=A+\left(\frac{y}{10}\right)$$
3	1 2	syl5eq	Could not format ( x = A -> _ x y = ( A + ( y / ; 1 0 ) ) ) : No typesetting found for |- ( x = A -> _ x y = ( A + ( y / ; 1 0 ) ) ) with typecode |-
4		oveq1	$$⊢y=B\to \frac{y}{10}=\frac{B}{10}$$
5	4	oveq2d	$$⊢y=B\to A+\left(\frac{y}{10}\right)=A+\left(\frac{B}{10}\right)$$
6		df-dp2	Could not format _ A B = ( A + ( B / ; 1 0 ) ) : No typesetting found for |- _ A B = ( A + ( B / ; 1 0 ) ) with typecode |-
7	5 6	eqtr4di	Could not format ( y = B -> ( A + ( y / ; 1 0 ) ) = _ A B ) : No typesetting found for |- ( y = B -> ( A + ( y / ; 1 0 ) ) = _ A B ) with typecode |-
8		df-dp	Could not format . = ( x e. NN0 , y e. RR |-> _ x y ) : No typesetting found for |- . = ( x e. NN0 , y e. RR |-> _ x y ) with typecode |-
9	6	ovexi	Could not format _ A B e. _V : No typesetting found for |- _ A B e. _V with typecode |-
10	3 7 8 9	ovmpo	Could not format ( ( A e. NN0 /\ B e. RR ) -> ( A . B ) = _ A B ) : No typesetting found for |- ( ( A e. NN0 /\ B e. RR ) -> ( A . B ) = _ A B ) with typecode |-