Definition df-dp2 32854

Description: Define the "decimal fraction constructor", which is used to build up "decimal fractions" in base 10. This is intentionally similar to df-dec 12734. (Contributed by David A. Wheeler, 15-May-2015.) (Revised by AV, 9-Sep-2021.)

Assertion

Ref	Expression
df-dp2	⊢ _𝐴𝐵 = (𝐴 + (𝐵 / ;10))

Detailed syntax breakdown of Definition df-dp2

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2		cB	. . 3 class 𝐵
3	1, 2	cdp2 32853	. 2 class _𝐴𝐵
4		c1 11156	. . . . 5 class 1
5		cc0 11155	. . . . 5 class 0
6	4, 5	cdc 12733	. . . 4 class ;10
7		cdiv 11920	. . . 4 class /
8	2, 6, 7	co 7431	. . 3 class (𝐵 / ;10)
9		caddc 11158	. . 3 class +
10	1, 8, 9	co 7431	. 2 class (𝐴 + (𝐵 / ;10))
11	3, 10	wceq 1540	1 wff _𝐴𝐵 = (𝐴 + (𝐵 / ;10))

This definition is referenced by:  dp2eq1  32855  dp2eq2  32856  dp20u  32860  dp20h  32861  dp2cl  32862  dp2clq  32863  rpdp2cl  32864  dp2lt10  32866  dp2lt  32867  dp2ltsuc  32868  dp2ltc  32869  dpval  32872  dpfrac1  32874  dpval2  32875  dpval3  32876  dp3mul10  32880